Question

The equation of the perpendicular bisector of the segment with endpoints (-4, -2) and (8, 4) can be written as ( ), which simplifies to

Answer 1

The equation of the perpendicular bisector of the segment with endpoints (-4, -2) and (8, 4) can be written as y - 1 = -2(x - 2) which simplifies to y = -2x + 5.

What is the equation of a perpendicular bisector?

Find the Midpoint:

`\[ \left((-4 + 8)/(2), (-2 + 4)/(2)\right) = (2, 1) \]`

Find the slope of the original segment:

`\[ m = (4 - (-2))/(8 - (-4)) = (6)/(12) = (1)/(2) \]`

Find the negative reciprocal of the slope:

`\[ m_{\text{perpendicular}} = -(1)/((1)/(2)) = -2 \]`

Now, use the point-slope form with the midpoint (2, 1) and the slope 2:

y - 1 = -2(x - 2)

Simplify:

y - 1 = -2x + 4

Now, express it in the form y = mx + b:

y = -2x + 5

So, the equation of the perpendicular bisector is y = -2x + 5.

Complete Question:

The equation of the perpendicular bisector of the segment with endpoints (-4, -2) and (8, 4) can be written as ......................... which simplifies to .....................