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)

Step-by-step explanation

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

`(x_m,y_m)=((x_1+x_2)/(2),(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=(x_1+x_2)/(2)`

Substitute the values into the above.

`-4=(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=(y_1+y_2)/(2)`

Substitute the values.

`7=(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).