Question

the midpoint of $overline{st}$ is $m(7.5, 13)$. one endpoint is $s(14, 10)$. find the coordinates of the other endpoint $t$. write the coordinates as decimals or integers. $t = (box box)$

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 $S(x_1,y_1)=(14,10)$ and $T(x_2,y_2)$. The mid - point $M(7.5,13)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=7.5$. Substitute $x_1 = 14$ into the equation: $\frac{14 + x_2}{2}=7.5$. Multiply both sides by 2: $14+x_2 = 15$. Then subtract 14 from both sides: $x_2=15 - 14=1$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=13$. Substitute $y_1 = 10$ into the equation: $\frac{10 + y_2}{2}=13$. Multiply both sides by 2: $10 + y_2=26$. Then subtract 10 from both sides: $y_2=26 - 10 = 16$.

Answer:

$(1,16)$