Question

the midpoint of $overline{pq}$ is $m=(3,4)$. 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 $M=(3,4)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=3$. Substitute $x_1 = 6$ into the equation: $\frac{6+x_2}{2}=3$. Multiply both sides by 2: $6 + x_2=6$. Then subtract 6 from both sides: $x_2=0$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=4$. Substitute $y_1 = 2$ into the equation: $\frac{2+y_2}{2}=4$. Multiply both sides by 2: $2 + y_2=8$. Then subtract 2 from both sides: $y_2 = 6$.

Answer:

$(0,6)$