Question

w has a mid - point at m(12.5, - 19). point w is at (69, 57). find the coordinates of point v. write the coordinates as decimals or integers. v=( , )

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 the coordinates of $V$ be $(x,y)$ and of $W$ be $(x_2,y_2)=(69,57)$ and of $M$ be $(x_m,y_m)=(12.5,-19)$.

Step2: Solve for $x$

We know that $x_m=\frac{x + x_2}{2}$. Substituting the values, we get $12.5=\frac{x + 69}{2}$. Multiply both sides by 2: $2\times12.5=x + 69$. So, $25=x + 69$. Then $x=25 - 69=-44$.

Step3: Solve for $y$

We know that $y_m=\frac{y + y_2}{2}$. Substituting the values, we get $-19=\frac{y + 57}{2}$. Multiply both sides by 2: $2\times(-19)=y + 57$. So, $-38=y + 57$. Then $y=-38 - 57=-95$.

Answer:

$(-44,-95)$