Question

The midpoint of AB is M(-1,-5). If the coordinates of A are (4, -3), what arethe coordinates of B?

Answer 1

ANSWER

(-6, -7)

EXPLANATION

We have that the midpoint of A and B is M (-1, -5).

The midpoint, M, of two points A(x1, y1) and B(x2, y2) is given as:

$M\text{ = (}\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})_{}$

We are given that:

(x1, y1) = (4, -3)

We need to find (x2, y2).

$\Rightarrow\text{ (-1, -5) = (}\frac{4+x_2}{2},\text{ }\frac{-3+y_2}{2})$

Now, compare the x and y cordinates separately.

For x:

$\begin{gathered} -1\text{ = }\frac{4+x_2}{2} \\ \Rightarrow\text{ -1 }\cdot2=4+x_2 \\ -2=4+x_2 \\ \Rightarrow x_2\text{ = -2 + -4} \\ x_2\text{ = -6} \end{gathered}$

For y:

$\begin{gathered} -5\text{ = }\frac{-3+y_2}{2} \\ \Rightarrow\text{ -5 }\cdot2=-3+y_2 \\ -10=-3+y_2 \\ y_2\text{ = -10 + 3} \\ y_2\text{ = -7} \end{gathered}$

So, the cordinates of B are (-6, -7)