Question

The midpoint of AB is (-4,7) and point A is(1,8)What are the coordinates of the other endpoint, B?

Answer 1

The coordinates of the other endpoint B are (-9, 6)

EXPLANATION

The midpoint of a point can be calculated using the formula below:

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

Let (x₂ , y₂ ) be the coodinates of endpoint B.

From the given equation;

Xm = -4 Ym= 7 x₁= 1 y₁=8

We first solve for x₂.

$x_m=\frac{x_1+x_2}{2}$

Substitute the values into the above.

$-4=\frac{1+x_2}{2}$

Cross-multiply.

$-8=1+x_2$

Subtract 1 from both-side of the equation.

$-8-1=x_2$

$x_2=-9$

Similarly, solve for y₂

$y_m=\frac{y_1+y_2}{2}$

Substitute the values.

$7=\frac{8+y_2}{2}$

Cross-multiply

$14=8+y_2$

Subtract 8 from both-side of the equation.

$14-8=y_2$

$y_2=6$

The coordinates of the other endpoint B are (-9, 6).