Question

the midpoint of $overline{pq}$ is $m(5.5,1.5)$. one endpoint is $p(8,1)$. find the coordinates of the other endpoint $q$. write the coordinates as decimals or integers. q = ( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Given $M(5.5,1.5)$ and $P(8,1)$.

Step2: Solve for $x$ - coordinate of $Q$

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 8$ and $x_M=5.5$, we get $\frac{8 + x_2}{2}=5.5$. Multiply both sides by 2: $8 + x_2=11$. Then subtract 8 from both sides: $x_2=11 - 8=3$.

Step3: Solve for $y$ - coordinate of $Q$

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 1$ and $y_M = 1.5$, we get $\frac{1 + y_2}{2}=1.5$. Multiply both sides by 2: $1 + y_2=3$. Then subtract 1 from both sides: $y_2=3 - 1=2$.

Answer:

$(3,2)$