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((x_A+x_B)/(2),\ (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:

`(-1+x_B)/(2)=5\qquad|\cdot2\\\\-1+x_B=10\qquad|+1\\\\x_B=11\\\\(4+y_B)/(2)=4\qquad|\cdot2\\\\4+y_B=8\qquad|-4\\\\y_B=4`

Answer: B(11, 4).