Question

the mid - point of vw is m(3, - 4). one endpoint is w(6, 2). find the coordinates of the other endpoint 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 $V=(x,y)$, $W=(6,2)$ and $M=(3,-4)$.

Step2: Solve for x - coordinate of V

We know that $\frac{x + 6}{2}=3$. Cross - multiply: $x + 6=6$. Then subtract 6 from both sides: $x=0$.

Step3: Solve for y - coordinate of V

We know that $\frac{y + 2}{2}=-4$. Cross - multiply: $y+2=-8$. Then subtract 2 from both sides: $y=-10$.

Answer:

$(0,-10)$