Question

the midpoint of (overline{tu}) is (m(-11.5, -4.5)). one endpoint is (t(-16, 8)). find the coordinates of the other endpoint (u). write the coordinates as decimals or integers. (u = (space,space))

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 $T(x_1,y_1)=(-16,8)$ and $U(x_2,y_2)$. The mid - point $M(-11.5,-4.5)$.

Step2: Find the x - coordinate of U

We know that $\frac{x_1 + x_2}{2}=-11.5$. Substitute $x_1=-16$ into the equation: $\frac{-16 + x_2}{2}=-11.5$. Multiply both sides by 2: $-16 + x_2=-23$. Then add 16 to both sides: $x_2=-23 + 16=-7$.

Step3: Find the y - coordinate of U

We know that $\frac{y_1 + y_2}{2}=-4.5$. Substitute $y_1 = 8$ into the equation: $\frac{8 + y_2}{2}=-4.5$. Multiply both sides by 2: $8 + y_2=-9$. Then subtract 8 from both sides: $y_2=-9 - 8=-17$.

Answer:

$(-7,-17)$