Question

vw has a midpoint at m(-13, -8). point v is at (-16, 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 between 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 $V(x_1,y_1)=(-16,2)$ and $W(x_2,y_2)$, and $M(-13,-8)$.

Step2: Solve for the x - coordinate of W

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting the known values: $\frac{-16 + x_2}{2}=-13$. Multiply both sides by 2: $-16 + x_2=-26$. Then add 16 to both sides: $x_2=-26 + 16=-10$.

Step3: Solve for the y - coordinate of W

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting the known values: $\frac{2 + y_2}{2}=-8$. Multiply both sides by 2: $2 + y_2=-16$. Then subtract 2 from both sides: $y_2=-16 - 2=-18$.

Answer:

$W=(-10,-18)$