Question

the midpoint m of $overline{vw}$ has coordinates (-4, -2.5). point w has coordinates (-4, -12). find the coordinates of point v. write the coordinates as decimals or integers. v = ( )

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 $V$ be $(x,y)$ and the coordinates of $W$ be $(-4,-12)$ and the mid - point $M$ be $(-4,-2.5)$.

Step2: Solve for x - coordinate

We have $\frac{x+( - 4)}{2}=-4$. Multiply both sides by 2: $x - 4=-8$. Then add 4 to both sides: $x=-4$.

Step3: Solve for y - coordinate

We have $\frac{y+( - 12)}{2}=-2.5$. Multiply both sides by 2: $y-12 = - 5$. Then add 12 to both sides: $y = 7$.

Answer:

$(-4,7)$