Question

the midpoint of tu is m(13.5, 10.5). one endpoint is t(18, 2). find the coordinates of the other endpoint u. write the coordinates as decimals or integers. u = ( , )

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 $T(x_1,y_1)=(18,2)$ and $U(x_2,y_2)$. Given $M(x_m,y_m)=(13.5,10.5)$.

Step2: Solve for $x$ - coordinate of $U$

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, $13.5=\frac{18 + x_2}{2}$. Multiply both sides by 2: $2\times13.5=18 + x_2$. So, $27=18 + x_2$. Then $x_2=27 - 18=9$.

Step3: Solve for $y$ - coordinate of $U$

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, $10.5=\frac{2 + y_2}{2}$. Multiply both sides by 2: $2\times10.5=2 + y_2$. So, $21=2 + y_2$. Then $y_2=21 - 2 = 19$.

Answer:

$(9,19)$