Question

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

Answer 1

Answer:

Other Endpoint (x₂,y₂) = (16,25)

Step-by-step 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

$M(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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

Using formula and finding (x₂,y₂)

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

So, x₂=16 and  y₂=25.

So, Other Endpoint (x₂,y₂) = (16,25)