Question

A segment has endpoints -4, -3 and 2, -9. Which equation represents the perpendicular bisector of the segment?

a. y = x - 3
b. y = -x - 3
c. x = -1
d. x = 3

Answer 1

The equation that represents the perpendicular bisector of the segment with endpoints -4, -3 and 2, -9 is y = x - 5.

Step-by-step explanation:

The equation that represents the perpendicular bisector of the segment with endpoints -4, -3 and 2, -9 can be found by finding the midpoint of the segment and then determining the negative reciprocal slope of the segment. To find the midpoint, we can use the formula:

xm = (x1 + x2) / 2

ym = (y1 + y2) / 2

Using the given endpoints, we have:

xm = (-4 + 2) / 2 = -1

ym = (-3 + -9) / 2 = -6

So, the midpoint of the segment is (-1, -6). Now, let's determine the slope of the segment:

m = (y2 - y1) / (x2 - x1)

m = (-9 - (-3)) / (2 - (-4)) = -6 / 6 = -1

The negative reciprocal of -1 is 1. Therefore, the slope of the perpendicular bisector is 1. Since the perpendicular bisector passes through the midpoint (-1, -6), the equation of the perpendicular bisector is:

y = mx + b

-6 = 1(-1) + b

-6 = -1 + b

b = -5

Therefore, the equation of the perpendicular bisector is y = x - 5.