Question

st has a midpoint at m(3, -14.5). point s is at (5, -10). find the coordinates of point t. write the coordinates as decimals or integers. t = ( )

Explanation:

Step1: Recall mid - point formula

The mid - point formula between 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 $S(x_1,y_1)=(5,-10)$ and $T(x_2,y_2)$ and $M(3,-14.5)$.

Step2: Solve for the x - coordinate of T

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 5$ and $x_M=3$ into the formula:
$\frac{5 + x_2}{2}=3$. Multiply both sides by 2: $5 + x_2=6$. Then subtract 5 from both sides: $x_2=6 - 5=1$.

Step3: Solve for the y - coordinate of T

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1=-10$ and $y_M = - 14.5$ into the formula:
$\frac{-10 + y_2}{2}=-14.5$. Multiply both sides by 2: $-10 + y_2=-29$. Then add 10 to both sides: $y_2=-29 + 10=-19$.

Answer:

$(1,-19)$