Question

A perpendicular bisector, , is drawn through point C on .
If the coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6), the x-intercept of is
. Point lies on .

Answer 1

let (x,y) be the mid-point.
\[x=\frac{ -3+7 }{ 2 }=\frac{ 4 }{ 2}=2\]
\[y=\frac{ 2+6 }{ 2 }=\frac{ 8 }{ 2}=4\]
midpoint=(2,4)
slope of AB\[=\frac{ 6-2 }{ 7+3 }=\frac{ 4 }{ 10 }=\frac{ 2 }{5 }\]
slope of line perpendicular to AB=-5/2
eq. of line pependicular to AB through (2,4) is
\[y-4=-\frac{ 5 }{ 2 }(x-2)\]
2y-8=-5x+10
5x+2y=10+8
or
5x+2y=18
perpendicular bisector of AB lies on line 5x+2y=18

Answer 2

thank you