Question

st has a mid - point at m(10, 9). point t is at (10, 8). 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 $(x,y)$, point $T(10,8)$ and mid - point $M(10,9)$.

Step2: Solve for $x$

For the $x$ - coordinate of the mid - point: $\frac{x + 10}{2}=10$. Multiply both sides by 2: $x + 10=20$. Subtract 10 from both sides: $x=10$.

Step3: Solve for $y$

For the $y$ - coordinate of the mid - point: $\frac{y + 8}{2}=9$. Multiply both sides by 2: $y + 8 = 18$. Subtract 8 from both sides: $y = 10$.

Answer:

$(10,10)$