Geometry Problems on a Coordinate Plane

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Questions

• What is the definition of a coordinate proof? And what is an example?
• How would you do coordinate geometry proofs?
• What is the slope of the line through P(6, −6) and Q(8, −1)?
• Find the slope of the line through P(−5, 1) and Q(9, −5)?
• What is the slope of the line through P(2, 8) and Q(0, 8)?
• What is the an equation of the line that goes through (−1, −3) and is perpendicular to the line #2x + 7y + 5 = 0#?
• What is an equation of the line that goes through point (8, −9) and whose slope is undefined?
• Given two ordered pairs (1,-2) and (3,-8), what is the equation of the line in slope-intercept form?
• How would you solve the system of these two linear equations: #2x + 3y = -1# and #x - 2y = 3#? Enter your solution as an ordered pair (x,y).
• Which of the ordered pairs forms a linear relationship: (-2,5) (-1,2) (0,1) (1,2)? Why?
• What is the radius of a circle given by the equation #(x+1)^2+(y-2)^2=64#?
• Find the vertex and axis of symmetry of this: #y = -3 (x + 4)^2 +2#?
• What is the line of intersection between the planes #3x+y-4z=2# and #x+y=18#?
• How do you find the angle between the planes #x + 2y - z + 1 = 0# and #x - y + 3z + 4 = 0#?
• Can two lines (each on a different plane) intersect?
• Are the planes #x+y+z=1# , #x-y+z=1# parallel, perpendicular, or neither? If neither, what is the angle between them?
• What is the distance between the planes #2x – 3y + 3z = 12# and #–6x + 9y – 9z = 27#?
• How do you determine if two vectors lie in parallel planes?
• How do I calculate the distance between the two parallel planes #x - 2y + 2z = 7# and #2y - x - 2z = 2#?
• How can planes intersect?
• What are the parametric equations for the line of intersection of the planes #x + y + z = 7# and #x + 5y + 5z = 7#?
• How do I find the angle between the planes #x + 2y − z + 1 = 0# and #x − y + 3z + 4 = 0#?
• What are the equations of the planes that are parallel to the plane #x+2y-2z=1# and two units away from it?
• Find the intersection point between #x^2+y^2-4x-2y=0# and the line #y=x-2# and then determine the tangent that those points?
• Question #ed0b6
• Question #6de4a
• Let M be a matrix and u and v vectors: #M =[(a, b),(c, d)], v = [(x), (y)], u =[(w), (z)].# (a) Propose a definition for #u + v#. (b) Show that your definition obeys #Mv + Mu = M(u + v)#?
• Let M and N be matrices , #M = [(a, b),(c,d)] and N =[(e, f),(g, h)],# and #v# a vector #v = [(x), (y)].# Show that #M(Nv) = (MN)v#?
• Given #C_1->y^2+x^2-4x-6y+9=0#, #C_2->y^2+x^2+10x-16y+85=0# and #L_1->x+2y+15=0#, determine #C->(x-x_0)^2+(y-y_0)^2-r^2=0# tangent to #C_1,C_2# and #L_1#?
• Given #L_1->x+3y=0#, #L_2=3x+y+8=0# and #C_1=x^2+y^2-10x-6y+30=0#, determine #C->(x-x_0)^2+(y-y_0)^2-r^2=0# tangent to #L_1,L_2# and #C_1#?
• The equations #{(y = c x^2+d, (c > 0, d < 0)),(x = a y^2+ b, (a > 0, b < 0)):}# have four intersection points. Prove that those four points are contained in one same circle ?
• What are two lines in the same plane that intersect at right angles?
• Given the surface #f(x,y,z)=y^2 + 3 x^2 + z^2 - 4=0# and the points #p_1=(2,1,1)# and #p_2=(3,0,1)# determine the tangent plane to #f(x,y,z)=0# containing the points #p_1# and #p_2#?
• What is the equation of the line passing through (-3,-2 ) and (1, -5)?
• How do we find out whether four points #A(3,-1,-1),B(-2,1,2)#, #C(8,-3,0)# and #D(0,2,-1)# lie in the same plane or not?
• If the planes #x=cy+bz# , #y=cx+az# , #z=bx+ay# go through the straight line, then is it true that #a^2+b^2+c^2+2abc=1#?
• How to determine the coordinates of the point M?#A_(((2,-5)));B_(((-3,5)))#;And #vec(BM)=1/5vec(AB)#
• Question #50ea4
• Is my teacher's final answer wrong?