Question

The midpoint of AB is M(-4,-3). If the coordinates of A are (-1, -2), what
are the coordinates of B?

Answer 1

Answer:

$B(-7,-4)$

Step-by-step explanation:

Let the co-ordinates of B be $(x_{2},y_{2})$

If a point $M(x,y)$ is a mid-point of line segment AB with $A(x_{1},y_{1})$ and  $B(x_{2},y_{2})$, then:

$x=\frac{x_{1}+x_{2}}{2}\\y=\frac{y_{1}+y_{2}}{2}$

Here, $M(x,y)$ is $M(-4,-3), A(x_{1},y_{1})$ is $A(-1,-2)$.

So, $x = -4, y = -3, x_{1} = -1, y_{1}=-2$

Plug in the formula and solve for unknowns.

$x=\frac{x_{1}+x_{2}}{2}\\-4=\frac{-1+x_{2}}{2}\\x_{2}=-8+1=-7\\\\y=\frac{y_{1}+y_{2}}{2}\\-3=\frac{-2+y_{2}}{2}\\y_{2}=-6+2=-4$

Therefore, the co-ordinates of point B are $B(-7,-4)$