Question

Find the equation of the perpendicular bisector drawn to the side BC of $\Delta ABC$, whose vertices are $A(-2,1),B(2,3)$ and $C(4,5)$.

• A. $x+y=7$
• B. $x-y=5$
• C. $x-y=7$
• D. $x+y=9$

Answer 1

The correct option is A $x+y=7$

Given vertices of triangle ABC

$A(-2,1),B(2,3),C(4,5)$

The perpendicular bisector on BC at point D then D is the mid point of BC

By Midpoint formula

$X=\left(\frac{x_1+x_2}{2}\right)andY=\left(\frac{y_1+y_2}{2}\right)$

D$(3,4)$

Slope of side BC $=\frac{5-3}{4-2}=1$

The slope of perpendicular bisector be $m=-1$

$m=-1$

Equation of perpendicular bisector from point D and Slope m

$y-4=-1(x-3)$

$y-4=-x+3$

$x+y=7$