Question

the midpoint m of $overline{st}$ has coordinates (-6.75, 10.5). point t has coordinates (-9.3, 10.5). 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 $(x_T,y_T)=( - 9.3,10.5)$ and the coordinates of the mid - point $M$ be $(x_M,y_M)=( - 6.75,10.5)$.

Step2: Solve for the x - coordinate of S

We know that $x_M=\frac{x + x_T}{2}$. Substituting the known values, we have $-6.75=\frac{x+( - 9.3)}{2}$. Multiply both sides by 2: $-6.75\times2=x - 9.3$. So, $-13.5=x - 9.3$. Add 9.3 to both sides: $x=-13.5 + 9.3=-4.2$.

Step3: Solve for the y - coordinate of S

We know that $y_M=\frac{y + y_T}{2}$. Substituting the known values, $10.5=\frac{y + 10.5}{2}$. Multiply both sides by 2: $10.5\times2=y + 10.5$. So, $21=y + 10.5$. Subtract 10.5 from both sides: $y=21 - 10.5 = 10.5$.

Answer:

$(-4.2,10.5)$