How to answer this questions: coordinates of the midpoints and finding the equations of lines AC?
1 Answer
Explanation:
(a)
"given "A(x_1,y_1)" and "B(x_2,y_2)
"then the coordinates of the midpoint (M) of AB"
•color(white)(x)M=[1/2(x_1+x_2),1/2(y_1+y_2)]
rArrM=[1/2(9+5),1/2(10+0)]=(7,5)
rArrN=[1/2(9+13),1/2(10+0)]=(11,5)
(b)
"equations of lines AC and BC"
"the equation of a line in "color(blue)"slope-intercept form" is.
•color(white)(x)y=mx+b
"where m is the slope and b the y-intercept"
"calculate the slope m using the "color(blue)"gradient formula"
•color(white)(x)m=(y_2-y_1)/(x_2-x_1)
rArrm_(AC)=(10-0)/(9-5)=10/4=5/2
rArry=5/2x+blarrcolor(blue)"partial equation"
"to find b substitute the coordinates of either A or C"
"into the partial equation"
"using "A(5,0)" then"
0=25/2+brArrb=-25/2
rArry=5/2x-25/2larrcolor(blue)"equation of AC"
"Similarly for the equation of BC"
m_(BC)=(10-0)/(9-13)=10/(-4)=-5/2
rArry=-5/2x+b
"using "B(13,0)" then"
0=-65/2+brArrb=65/2
rArry=-5/2x+65/2larrcolor(blue)"equation of BC"