Question

st has a mid - point at m(9, 3). point t is at (8, 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 $S=(x_1,y_1)$ and $T=(x_2,y_2)=(8,5)$, and $M=(9,3)$.

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

We know that $\frac{x_1 + x_2}{2}=9$ and $x_2 = 8$. Substitute $x_2$ into the formula: $\frac{x_1+8}{2}=9$. Multiply both sides by 2: $x_1 + 8=18$. Then subtract 8 from both sides: $x_1=10$.

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

We know that $\frac{y_1 + y_2}{2}=3$ and $y_2 = 5$. Substitute $y_2$ into the formula: $\frac{y_1 + 5}{2}=3$. Multiply both sides by 2: $y_1+5 = 6$. Then subtract 5 from both sides: $y_1=1$.

Answer:

$(10,1)$