Question

the midpoint m of $overline{vw}$ has coordinates (-4, -3). point v has coordinates (2, -2). find the coordinates of point w. write the coordinates as decimals or integers. w = ( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $M=(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let the coordinates of point $W$ be $(x,y)$, $V(2,-2)$ and $M(-4,-3)$.

Step2: Solve for the x - coordinate of W

We know that $\frac{2 + x}{2}=-4$. Multiply both sides by 2: $2 + x=-8$. Then subtract 2 from both sides: $x=-8 - 2=-10$.

Step3: Solve for the y - coordinate of W

We know that $\frac{-2 + y}{2}=-3$. Multiply both sides by 2: $-2 + y=-6$. Then add 2 to both sides: $y=-6 + 2=-4$.

Answer:

$(-10,-4)$