Question

the mid - point of $pq$ is $m(2,7)$. one endpoint is $p(4,6)$. find the coordinates of the other endpoint $q$. write the coordinates as decimals or integers. $q=(square,square)$

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 $P(x_1,y_1)=(4,6)$ and $Q(x_2,y_2)$, and $M(2,7)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=2$. Substitute $x_1 = 4$ into the equation: $\frac{4+x_2}{2}=2$. Multiply both sides by 2: $4 + x_2=4$. Then subtract 4 from both sides: $x_2=0$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=7$. Substitute $y_1 = 6$ into the equation: $\frac{6 + y_2}{2}=7$. Multiply both sides by 2: $6+y_2 = 14$. Then subtract 6 from both sides: $y_2=8$.

Answer:

$(0,8)$