Question

Find the equation of the perpendicular bisector of the joining $(5,0)$ and $(-7,3)$

• A. $8x+2y+11=0$
• B. $8x-2y+11=0$
• C. $8x-y+11=0$
• D. $8x+y+11=0$

Answer 1

Answer: (B)

$8x-2y+11=0$

Let A(5,0) and B(-7,3)

Midpoint of $AB=(\frac{5-7}{2},\frac{0+3}{2})$

$=(-1,\frac{3}{2})$

Slope of line AB $=\frac{3-0}{-7-5}$

$=\frac{3}{-12}$

$=\frac{1}{-4}$

Thus, the slope of the perpendicular bisector $=\frac{-1}{\frac{1}{-4}}$

$=4$

The perpendicular bisector passes through $(-1,\frac{3}{2})$ and slope is 4

Thus,

Equation of the line is

$y-\frac{3}{2}=4(x-(-1\left)\right)$

$=>\frac{2y-3}{2}=4(x+1)$

$=>2y-3=8x+8$

$=>8x-2y+11=0$