Question

the midpoint of $overline{pq}$ is $m=(2,0)$. one endpoint is $p=(6, - 2)$. find the coordinates of the other endpoint, $q$.

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 $P=(x_1,y_1)=(6,-2)$ and $Q=(x_2,y_2)$, and $M=(2,0)$.

Step2: Solve for $x_2$

We have $\frac{x_1 + x_2}{2}=2$. Substitute $x_1 = 6$ into the equation: $\frac{6 + x_2}{2}=2$. Multiply both sides by 2: $6+x_2 = 4$. Then subtract 6 from both sides: $x_2=4 - 6=-2$.

Step3: Solve for $y_2$

We have $\frac{y_1 + y_2}{2}=0$. Substitute $y_1=-2$ into the equation: $\frac{-2 + y_2}{2}=0$. Multiply both sides by 2: $-2+y_2 = 0$. Then add 2 to both sides: $y_2 = 2$.

Answer:

$Q=(-2,2)$