Question

the midpoint m of st has coordinates (64.5, 39). point t has coordinates (69, 34). find the coordinates of point s. write the coordinates as decimals or integers. s = ( )

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 the coordinates of point $S$ be $(x,y)$ and the coordinates of point $T$ be $(69,34)$ and the mid - point $M$ be $(64.5,39)$.

Step2: Solve for $x$ (x - coordinate of $S$)

We know that $\frac{x + 69}{2}=64.5$. Multiply both sides by 2: $x + 69=129$. Then subtract 69 from both sides: $x=129 - 69=60$.

Step3: Solve for $y$ (y - coordinate of $S$)

We know that $\frac{y + 34}{2}=39$. Multiply both sides by 2: $y + 34 = 78$. Then subtract 34 from both sides: $y=78 - 34 = 44$.

Answer:

$(60,44)$