Question

Which points are on the perpendicular bisector of the given segment? Check all that apply. (−8, 19) (1, −8) (0, 19) (−5, 10) (2, −7)

Answer 1

Answer:

−8, 19

1, −8

-5, 10

Step-by-step explanation:

Answer 2

The points that are on the perpendicular bisector of the given segment is (-5, 10)

What is the perpendicular bisector?

Perpendicular bisector is defined as a line that divide an angle into  two equal parts at 90 degrees.

The standard equation of a line in point-slope form is expressed as

y-y₁ = m(x-x₁)

First, we need to get the equation of the line using the coordinates (-20, 0) and (10, 15)

Get the slope of the line

m = 15-0/10-(-20)

m = 15/30

m = 1/2

The slope of the line perpendicular to the line is -2

Using the point (-5, 10) on the line, get the equation in the point-slope form:

y - 10 = -2(x + 5)

y - 10 = -2x - 10

y + 2x = -10 + 10

y + 2x = 0

y = -2x

To check which points are on the perpendicular bisector of the given segment, hence;

For the coordinate (-8, 19)

19 = -2(-8)

19 ≠ 16 (This is not a solution)

For the coordinate (1, -8)

-8 = -2(1)

-8 ≠ -2 (This is not a solution)

For the coordinate (-5, 10)

10 = -2(-5)

10 = 10 (This is a solution)

Hence, the point that is on the perpendicular bisector of the given segment is (-5, 10)

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