Question

HELP PLS.

A line segment has an endpoint at (4, 5). If the
midpoint of the line segment is (-1,4), what is the
location of the line segment's other endpoint?

Answer 1

Answer: (-6, 3)

=========================================================

Step-by-step explanation:

A = (4,5) is one endpoint

B = (-1, 4) is the midpoint

C = (x,y) is the other endpoint

For now, focus on the x coordinates of each point

A and C have x coordinates of 4 and x respectively

Add them up and divide in half. Set this equal to the x coordinate of B

(4+x)/2 = -1

4+x = 2*(-1)

4+x = -2

x = -2-4

x = -6 which is the x coordinate of point C

Repeat this same idea for the y coordinates

(5+y)/2 = 4

5+y = 2*4

5+y = 8

y = 8-5

y = 3 which is the y coordinate of point C

Therefore, point C is located at (-6, 3)

--------------------------

To verify the answer, you can use the distance formula to calculate the following segment lengths: AB and BC

You should find that AB = BC. This is because the midpoint splits segment AC into two smaller equal pieces.

Another way to verify the answer is to use the midpoint formula on points A(4,5) and C(-6,3). The result of using this formula should be B(-1,4) mentioned earlier.