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
[tex]M(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
We have [tex]x_1=4 , y_1= -9 , x_m=10, y_m=8[/tex]
Using formula and finding (x₂,y₂)
[tex]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[/tex]
So, x₂=16 and y₂=25.
So, Other Endpoint (x₂,y₂) = (16,25)
