Question

the midpoint of $overline{st}$ is $m(3.5, 13)$. one endpoint is $s(0, 11)$. find the coordinates of the other endpoint $t$. write the coordinates as decimals or integers. $t=(square,square)$

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 $S(x_1,y_1)=(0,11)$ and $T(x_2,y_2)$, and $M(3.5,13)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=3.5$. Substitute $x_1 = 0$ into the equation: $\frac{0 + x_2}{2}=3.5$. Multiply both sides by 2: $x_2=7$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=13$. Substitute $y_1 = 11$ into the equation: $\frac{11 + y_2}{2}=13$. Multiply both sides by 2: $11 + y_2 = 26$. Then subtract 11 from both sides: $y_2=15$.

Answer:

$(7,15)$