Question

Find anequation for the perpendicular bisector of the line segment whose endpointsare (-8, 4) and (-4,-4).

Answer 1

y = 1/2(x) - 1

To solve this question, we would use the midpoint formula to find the x and y coordinates.

Mid point formula:

$\begin{gathered} \frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2} \\ =\text{ }\frac{-4+8}{2},\text{ }\frac{-4+4}{2} \\ =\text{ 2, 0} \end{gathered}$

Midpoint = (2,0)

Then we would find the slope:

$\begin{gathered} slope\text{ = m = }\frac{y_{2-}y_1}{x_{2\text{ }}-x_1} \\ m\text{ = }\frac{-4-4}{-4+8} \\ m\text{ = }\frac{-8}{4}\text{ = }-2 \end{gathered}$

Since the slope = -2, the negative reciprocal of slopes give perpendicular.

the reciprocal = -1/-2 = 1/2

Then we apply linear quation- the slope intercept form to get the constant (c):

y = mx + c

from our midpoint (2,0), y = 0 and x =2

0 = 1/2(2) + c

c = -1

The equation for the perpendicular bisector:

y = 1/2(x) - 1