Question

the midpoint m of $overline{uv}$ has coordinates (-10.5, -8). point u has coordinates (-11, -4). 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 $U(x_1,y_1)$ and $V(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(-10.5,-8)$ and $U(-11,-4)$. Let the coordinates of $V$ be $(x,y)$.

Step2: Solve for $x$ - coordinate of $V$

We have $\frac{-11 + x}{2}=-10.5$. Multiply both sides by 2: $-11 + x=-21$. Then add 11 to both sides: $x=-21 + 11=-10$.

Step3: Solve for $y$ - coordinate of $V$

We have $\frac{-4 + y}{2}=-8$. Multiply both sides by 2: $-4 + y=-16$. Then add 4 to both sides: $y=-16 + 4=-12$.

Answer:

$(-10,-12)$