Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are (4,−1) and (8,7).

Answer 1

Answer:
`y=-(1)/(2)x+6`

Explanation:

The slope of the line segment is
`(-1-7)/(4-8)=2`.

• So, the slope of the perpendicular bisector is -1/2.

The midpoint of the line segment is
`\left((4+8)/(2), (-1+7)/(2) \right)=(6, 3)`.

Thus, the equation is:

`y-3=-(1)/(2)(x-6)\\\\y-3=-(1)/(2)x+3\\\\y=-(1)/(2)x+6`