Question

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (-2, -6) Midpoint: (-5, 1)

Answer 1

Answer:

(-8,8)

Step-by-step explanation:

The midpoint $M(x_M,y_M)$ of the segment AB with endpoints $A(x_A,y_A)$ and $B(x_B,y_B)$ has coordinates

$x_M=\dfrac{x_A+x_B}{2}\\ \\y_M=\dfrac{y_A+y_B}{2}$

In your case, $A(-2,-6), \ M(-5,1),$ then

$-5=\dfrac{-2+x_B}{2}\Rightarrow -2+x_B=-10,\ x_B=-10+2=-8\\ \\1=\dfrac{-6+y_B}{2}\Rightarrow -6+y_B=2,\ y_B=2+6=8$