Question

Find the other endpoint of the line segment with the given endpoint and midpoint.

Endpoint: (4,-9)
Midpoint: (10,8)

Answer 1

Other Endpoint (x₂,y₂) = (16,25)

Explanation:

We are given endpoint = (4,-9) and midpoint(10,8) we need to find the other endpoint of line segment.

Let other endpoint be (x₂,y₂)

The formula used to find other endpoint is using formula of midpoint

`M(x_m,y_m)=((x_1+x_2)/(2),(y_1+y_2)/(2))`

We have
`x_1=4 , y_1= -9 , x_m=10, y_m=8`

Using formula and finding (x₂,y₂)

`M(x_m,y_m)=((x_1+x_2)/(2),(y_1+y_2)/(2))\\(10,8)=((4+x_2)/(2),(-9+y_2)/(2))\\10=(4+x_2)/(2) , 8=(-9+y_2)/(2)\\Finding\ x_2\\10*2=4+x_2 \\20=4+x_2\\x_2=20-4, \\x_2=16\\Finding \ y_2\\8*2=-9+y_2\\16=-9+y_2\\y_2=16+9\\y_2=25`

So, x₂=16 and y₂=25.

So, Other Endpoint (x₂,y₂) = (16,25)