Question

Find the coordinate of B if A is the point (-1,4) and the midpoint is m=(5,4).

Answer 1

The formula of a midpoint:

$M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)$

We have:

$A(-1,\ 4)\to x_A=-1,\ y_A=4\\M(5,\ 4)\to x_M=5,\ y_M=4$

Substitute:

$\dfrac{-1+x_B}{2}=5\qquad|\cdot2\\\\-1+x_B=10\qquad|+1\\\\x_B=11\\\\\dfrac{4+y_B}{2}=4\qquad|\cdot2\\\\4+y_B=8\qquad|-4\\\\y_B=4$

Answer: B(11, 4).