Question

the midpoint of $overline{tu}$ is $m(8.5, -1)$. one endpoint is $t(17, -1)$. find the coordinates of the other endpoint $u$. write the coordinates as decimals or integers. $u = (square,square)$

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 $T(x_1,y_1)=(17,-1)$ and $U(x_2,y_2)$, and $M(8.5,-1)$.

Step2: Find the x - coordinate of U

We know that $\frac{x_1 + x_2}{2}=x_M$. Substitute $x_1 = 17$ and $x_M=8.5$ into the formula: $\frac{17 + x_2}{2}=8.5$. Multiply both sides by 2: $17+x_2 = 17$. Then subtract 17 from both sides: $x_2=0$.

Step3: Find the y - coordinate of U

We know that $\frac{y_1 + y_2}{2}=y_M$. Substitute $y_1=-1$ and $y_M = - 1$ into the formula: $\frac{-1 + y_2}{2}=-1$. Multiply both sides by 2: $-1+y_2=-2$. Then add 1 to both sides: $y_2=-1$.

Answer:

$(0,-1)$