Perpendicular Bisectors

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Questions

• What is a perpendicular bisector?
• What is the difference between medians, perpendicular bisectors, and altitudes?
• What is an example of a real world situation that implies the perpendicular bisector theorem?
• How do you find the perpendicular bisectors of a triangle?
• How do you write the equation of the perpendicular bisector of the segment with the given endpoints #(2,5)# and #(4,9)#?
• How do you find the equation for the perpendicular bisector of the segment with endpoints #(-1,-3)# and #(7,1)#?
• How do I find the equation of a perpendicular bisector of a line segment with the endpoints #(-2, -4)# and #(6, 4)#?
• What is the difference between a bisector and a perpendicular bisector?
• Given point A #(-2,1)# and point B #(1,3)#, how do you find the equation of the line perpendicular to the line AB at its midpoint?
• How do I write an equation for the perpendicular bisector of the segment joining the points #(5,-4)# and #(-3,-2)#?
• What is the equation of the perpendicular bisector of a chord of a circle?
• What is the perpendicular bisector of a line with points at A #(-33, 7.5)# and B #(4,17)#?
• How do you find the equation of the perpendicular bisector of the points #(1,4)# and #(5,-2)#?
• How do you find the equation of the perpendicular bisector of the segment joining the points A #(6, -3)# and B #(-2, 5)#?
• How do you find the equation that is the perpendicular bisector of the line segment with endpoints #(-2, 4)# and #(6, 8)#?
• How do you construct perpendicular bisectors of a triangle?
• How do you find the perpendicular bisector of a line segment?
• How many perpendicular bisectors can be constructed for a line?
• A triangle has corners at #(4 , 1 )#, ( 2, 4 )#, and #( 0, 2 )#. What are the endpoints of the triangle's perpendicular bisectors?
• A triangle has corners at #(6 , 1 )#, ( 4, 2 )#, and #( 2, 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(5 , 4 )#, ( 7, 1 )#, and #( 1, 3 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(2 , 4 )#, ( 3, 1 )#, and #( 8, 3 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(2 , 2 )#, ( 5, 6 )#, and #( 1, 4 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(2 , 8 )#, ( 2, 3 )#, and #( 5, 4 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(2 , 5 )#, ( 1, 3 )#, and #( 8, 1 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(5 , 3 )#, ( 7 ,8)#, and #( 2, 1 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(2 , 1 )#, ( 5 , 6)#, and #( 8 , 5 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has vertices at #A(a,b )#, #C(c,d)#, and #O(0,0)#. What are the endpoints and length of the perpendicular bisector of AC ?
• A triangle has corners at #(3,7)#, #(4,1)#, and #(8,2)#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(8 , 4 )#, ( 4 , 3)#, and #( 6 , 5 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• A triangle has corners at #(5 , 4 )#, ( 7 , 9)#, and #( 5 , 8 )#. What are the endpoints and lengths of the triangle's perpendicular bisectors?
• Question #0994c
• A line segment is bisected by line with the equation # 6 y + 7 x = 4 #. If one end of the line segment is at #(2 ,4 )#, where is the other end?
• A line segment is bisected by line with the equation # 3 y - 3 x = 4 #. If one end of the line segment is at #(2 ,4 )#, where is the other end?
• A line segment is bisected by line with the equation # 3 y - 3 x = 1 #. If one end of the line segment is at #(2 ,5 )#, where is the other end?
• A line segment is bisected by line with the equation # 6 y - 2 x = 1 #. If one end of the line segment is at #(2 ,5 )#, where is the other end?
• A line segment is bisected by line with the equation # 6 y - 2 x = 1 #. If one end of the line segment is at #(4 ,1 )#, where is the other end?
• A line segment is bisected by line with the equation # 6 y - 7 x = 3 #. If one end of the line segment is at #(4 ,2 )#, where is the other end?
• A line segment is bisected by line with the equation # 6 y - 7 x = 3 #. If one end of the line segment is at #(7 ,2 )#, where is the other end?
• A line segment is bisected by a line with the equation # 3 y - 7 x = 3 #. If one end of the line segment is at #(7 ,8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #(7 ,8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #(7 ,3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 3 y - 8 x = 2 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 7 y + x = 7 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 7 y + x = 1 #. If one end of the line segment is at #(1 ,6 )#, where is the other end?
• A line segment is bisected by a line with the equation # -3 y + x = 1 #. If one end of the line segment is at #(1 ,6 )#, where is the other end?
• A line segment is bisected by a line with the equation # -3 y + 7 x = 1 #. If one end of the line segment is at #(9 ,2 )#, where is the other end?
• A line segment is bisected by a line with the equation # - y + 7 x = 1 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?
• A line segment is bisected by a line with the equation # - y + 3 x = 1 #. If one end of the line segment is at #(6 ,3 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 2 y + 3 x = 1 #. If one end of the line segment is at #(6 ,3 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 5 y + 3 x = 1 #. If one end of the line segment is at #(6 ,4 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 5 y + 2 x = 1 #. If one end of the line segment is at #(6 ,4 )#, where is the other end?
• A line segment is bisected by a line with the equation # 5 y + 2 x = 1 #. If one end of the line segment is at #(6 ,4 )#, where is the other end?
• A line segment is bisected by a line with the equation # 5 y + 2 x = 1 #. If one end of the line segment is at #(3 ,4 )#, where is the other end?
• A line segment is bisected by a line with the equation # 5 y -4 x = 1 #. If one end of the line segment is at #(3 ,4 )#, where is the other end?
• A line segment is bisected by a line with the equation # 5 y -4 x = 1 #. If one end of the line segment is at #(3 ,8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 2 y -4 x = 1 #. If one end of the line segment is at #(3 ,8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 2 y + 9 x = 3 #. If one end of the line segment is at #(3 ,2 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y + 9 x = 8 #. If one end of the line segment is at #(5 ,2 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y + x = 8 #. If one end of the line segment is at #(5 ,2 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y + x = 8 #. If one end of the line segment is at #(5 ,6 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y + x = 3 #. If one end of the line segment is at #(5 ,6 )#, where is the other end?
• A line segment is bisected by a line with the equation # -7 y + x = 3 #. If one end of the line segment is at #(1 ,6 )#, where is the other end?
• A line segment is bisected by a line with the equation # -7 y + 5 x = 1 #. If one end of the line segment is at #(1 ,4 )#, where is the other end?
• A line segment is bisected by a line with the equation # -7 y + 3 x = 1 #. If one end of the line segment is at #( 2 , 4 )#, where is the other end?
• A line segment is bisected by a line with the equation # -7 y + 3 x = 2 #. If one end of the line segment is at #( 2 , 4 )#, where is the other end?
• A line segment is bisected by a line with the equation # -7 y + 3 x = 2 #. If one end of the line segment is at #( 2 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # -6 y + 3 x = 2 #. If one end of the line segment is at #( 5 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # -6 y + 9 x = 2 #. If one end of the line segment is at #( 5 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # -6 y - x = 3 #. If one end of the line segment is at #( 5 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # -6 y - x = 3 #. If one end of the line segment is at #( 8 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 2 y - x = 1 #. If one end of the line segment is at #( 8 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 2 y - x = 2 #. If one end of the line segment is at #( 8 , 7 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 2 y - 5 x = 2 #. If one end of the line segment is at #( 8 , 7 )#, where is the other end?
• A line segment is bisected by a line with the equation # 2 y - 5 x = 2 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 2 y - 2 x = 2 #. If one end of the line segment is at #( 3 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y - 2 x = 3 #. If one end of the line segment is at #( 5 , 6 )#, where is the other end?
• A line segment is bisected by a line with the equation # 3 y - 7 x = 2 #. If one end of the line segment is at #( 8 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # 6 y + 5 x = 2 #. If one end of the line segment is at #( 5 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 3 y + 5 x = 2 #. If one end of the line segment is at #( 5 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 3 y + 5 x = 2 #. If one end of the line segment is at #( 1 , 4 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 4 y + x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?
• A line segment is bisected by a line with the equation # - y + 7 x = 1 #. If one end of the line segment is at #( 7 , 2 )#, where is the other end?
• A line segment is bisected by a line with the equation # - y + 4 x = 3 #. If one end of the line segment is at #( 2 , 6 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 9 y + 4 x = 6 #. If one end of the line segment is at #( 7 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 3 y + 4 x = 6 #. If one end of the line segment is at #( 3 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 3 y + 6 x = 6 #. If one end of the line segment is at #( 3 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 3 y + 6 x = 5 #. If one end of the line segment is at #( 3 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 3 y + 2 x = 5 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 3 y + 2 x = 2 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 3 y + 5 x = 2 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 3 y + 5 x = 8 #. If one end of the line segment is at #( 7 , 9 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 6 y + 5 x = 4 #. If one end of the line segment is at #( 2 , 5 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 6 y + 2 x = 4 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 6 y + 2 x = 3 #. If one end of the line segment is at #( 4 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # - 6 y + x = 3 #. If one end of the line segment is at #( 4 , 5 )#, where is the other end?
• A line segment is bisected by a line with the equation # 2 y + x = 7 #. If one end of the line segment is at #( 5 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 2 y + 3 x = 3 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y + 3 x = 8 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 1 , 8 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 8 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 7 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y - 2 x = 5 #. If one end of the line segment is at #( 7 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 9 y - 2 x = 5 #. If one end of the line segment is at #( 7 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 9 y + x = 5 #. If one end of the line segment is at #( 7 , 4 )#, where is the other end?
• A line segment is bisected by a line with the equation # 8 y + 5 x = 4 #. If one end of the line segment is at #( 1 , 3 )#, where is the other end?
• A line segment is bisected by a line with the equation # 8 y + 5 x = 4 #. If one end of the line segment is at #( 2 , 7 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y - 3 x = 2 #. If one end of the line segment is at #( 7 , 5 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y - 3 x = 2 #. If one end of the line segment is at #( 2 , 5 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y - 3 x = 2 #. If one end of the line segment is at #( 2 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y + 3 x = 2 #. If one end of the line segment is at #( 2 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y + 3 x = 4 #. If one end of the line segment is at #( 8 , 1 )#, where is the other end?
• A line segment is bisected by a line with the equation # 4 y + 3 x = 4 #. If one end of the line segment is at #( 8 , 9 )#, where is the other end?
• Describe and write an equation for the locus of points equidistant form #A(a_x, a_y) and B(b_x,b_y)#? Test what you derived for #P_A(-2,5) and P_B(6,1)? #
• Let #A(x_a,y_a)# and #B(x_b,y_b)# be two points in the plane and let #P(x,y)# be the point that divides #bar(AB)# in the ratio #k :1#, where #k>0#. Show that #x= (x_a+kx_b)/ (1+k)# and #y= (y_a+ky_b)/( 1+k)#?
• Let A be #(−3,5)# and B be #(5,−10))#. Find: (1) the length of segment #bar(AB)# (2) the midpoint #P# of #bar(AB)# (3) the point #Q# which splits #bar(AB)# in the ratio #2:5#?
• Let #l# be a line described by equation ax+by+c=0 and let #P(x,y)# be a point not on #l#. Express the distance, #d# between #l and P# in terms of the coefficients #a, b and c# of the equation of line?
• In a triangle ABC (figure) the points P and Q are selected in the sides AC and BC respectively in a way that PC is half of BC and QC is half of AC:#bar(PC)/bar(BC) = 1/2; bar(QC)/bar(AC)= 1/2#. Find #bar(PQ)# if the side #bar(Ab)# is 20?
• In a triangle ABC, AB=AC and D is a point on side AC such that BCxBC=ACxCD. How to prove that BD=BC?
• This question combines geometry and algebra. Refer to the geometrical construction, find the unknown values?
• Maya drives from New York City to Boston at a rate of 40 MPH and drives at a rate of 60 MPH on the return trip. What was his average speed for the entire trip? Use the Harmonic mean to compute? Construct the HM geometrically?
• Using a compass and straight edge only mark two points A and B. Draw the line #l# through them and find another point C on #l# such that AB = BC?
• Draw a line l and a point A not lying on l. Draw the line m that is passing through A and parallel to #l#?
• Draw a line #l# and two points A and B not lying on l. Make sure that the line #bar(AB)# is not perpendicular to #l#. Find the point C on #l# such that AC = BC?
• Construct a regular pentagon using a compass and straight edge? Explain each step
• Given 2 numbers #(a,b)# it is possible to perform geometrically the following algebraic operations: a+b, a−b, a*b, a/b. Use only a straight edge and compass to show each operation?
• Constructing the angle 75°?
• Let #P(x_1, y_1)# be a point and let #l# be the line with equation #ax+ by +c =0#. Show the distance #d# from #P->l# is given by: #d =(ax_1+ by_1 + c)/sqrt( a^2 +b^2)#? Find the distance #d# of the point P(6,7) from the line l with equation 3x +4y =11?
• Let #P(a,b) and Q(c,d)# be two points in the plane. Find the equation of the line #l# that is the perpendicular bisector of the line segment #bar(PQ)#?
• Q is the midpoint of GH¯¯¯¯¯¯ , GQ=2x+3, and GH=5x−5 . What is the length of GQ¯¯¯¯¯ ?
• Given #x^2 + 4x - 32 = 0# use geometric construction to determine roots? Generalize to #ax^2+bx+c=0# finding a geometric interpretation of a quadratic formula #(-b+- sqrt(b^2-4ac))/(2a)#?
• Prove the diagonals of a parallelogram bisect each other, i.e. #bar(AE) = bar(EC)# and #bar(BE) = bar(ED)# ?
• On the figure given show that #bar(OC)# is #sqrt(2)#?
• Question #a55ba
• In a #DeltaABC#, right angled at #A#, a point #D# is on side #AB#. Prove that #CD^2=BC^2+BD^2#?
• Question #2b5bb
• Question #f11e4
• Adina is constructing a line perpendicular to YJ←→. She has already constructed two arcs as shown. She moves her compass point to Y to construct an arc above the line. What must be true about the width of Adina’s compass opening before she draws the arc?
• Mayumi is constructing a line through point P that is perpendicular to RS←→. She places her compass on point P to construct an arc. What must be true about the width of the compass opening when Mayumi draws the arc?
• Natasha is constructing the bisector of PQ¯¯¯¯¯PQ¯. She has already constructed an arc as shown. What should Natasha do for her next step?
• ABC is a triangle whose sides AB = 6 cm, BC = 8 cm and AC = 12 cms. D is such a point situated on AC that angle ADB = angle ABC. Find the length of BD ?
• How to do this perpendicular bisector of a chord question?
• In triangle ABC, AB=AC.The circle through B touches the side AC at the mid-point D of AC, passes through a point P on AB. Prove that 4 ×AP = AB ?
• Question #43bfc
• Question #0583a
• Question #ad0e0
• In a #DeltaXYZ# having #X(-3,2)#, #Y(-5,-6)# and #Z(-5,0)#, is perpendicular bisector of #YZ# same as median from #X#?
• Perpendicular bisectors of sides of a triangle are #y=-x+4#, #y=-3x+6# and #y=-1/2x+7/2#. What is its centroid?