Question

the midpoint of $overline{uv}$ is $m(3, 11.5)$. one endpoint is $u(2, 7)$. find the coordinates of the other endpoint $v$. write the coordinates as decimals or integers. $v = (square,square)$

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 $U(2,7)=(x_1,y_1)$ and $V=(x_2,y_2)$, and $M(3,11.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=3$. Substitute $x_1 = 2$ into the equation: $\frac{2+x_2}{2}=3$. Multiply both sides by 2: $2 + x_2=6$. Then subtract 2 from both sides: $x_2=6 - 2=4$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=11.5$. Substitute $y_1 = 7$ into the equation: $\frac{7+y_2}{2}=11.5$. Multiply both sides by 2: $7 + y_2=23$. Then subtract 7 from both sides: $y_2=23 - 7 = 16$.

Answer:

$(4,16)$