Question

the midpoint of $overline{uv}$ is $m(5.5, 9.5)$. one endpoint is $u(8, 1)$. 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 $U(x_1,y_1)=(8,1)$ and $V(x_2,y_2)$, and $M(5.5,9.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=5.5$. Substitute $x_1 = 8$ into the equation: $\frac{8 + x_2}{2}=5.5$. Multiply both sides by 2: $8 + x_2=11$. Then subtract 8 from both sides: $x_2=11 - 8=3$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=9.5$. Substitute $y_1 = 1$ into the equation: $\frac{1 + y_2}{2}=9.5$. Multiply both sides by 2: $1 + y_2 = 19$. Then subtract 1 from both sides: $y_2=19 - 1=18$.

Answer:

$(3,18)$