Question

the midpoint m of $overline{st}$ has coordinates (-31.5, -7.5). point s has coordinates (-83, 78). find the coordinates of point t. write the coordinates as decimals or integers. t = ( , )

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 $S(x_1,y_1)=(-83,78)$ and $T(x_2,y_2)$. The mid - point $M(-31.5,-7.5)$.

Step2: Find the x - coordinate of T

We know that $\frac{x_1 + x_2}{2}=-31.5$. Substitute $x_1=-83$ into the equation: $\frac{-83 + x_2}{2}=-31.5$. Multiply both sides by 2: $-83 + x_2=-31.5\times2=-63$. Then solve for $x_2$: $x_2=-63 + 83 = 20$.

Step3: Find the y - coordinate of T

We know that $\frac{y_1 + y_2}{2}=-7.5$. Substitute $y_1 = 78$ into the equation: $\frac{78 + y_2}{2}=-7.5$. Multiply both sides by 2: $78 + y_2=-7.5\times2=-15$. Then solve for $y_2$: $y_2=-15 - 78=-93$.

Answer:

$(20,-93)$