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.

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $S(x_1,y_1)$ and $T(x_2,y_2)$ is $M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. We know $M(9,3)$ and $T(8,5)$. Let the coordinates of $S$ be $(x,y)$.

Step2: Solve for the x - coordinate of S

We have $\frac{x + 8}{2}=9$. Multiply both sides by 2: $x + 8=18$. Then subtract 8 from both sides: $x=18 - 8=10$.

Step3: Solve for the y - coordinate of S

We have $\frac{y + 5}{2}=3$. Multiply both sides by 2: $y + 5=6$. Then subtract 5 from both sides: $y=6 - 5 = 1$.

Answer:

$(10,1)$