Question

the mid - point of tu is m(2, 15). one endpoint is t(6, 12). find the coordinates of the other endpoint u. write the coordinates as decimals or integers.

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 $T(6,12)$ be $(x_1,y_1)$ and $U(x,y)$ be $(x_2,y_2)$ and $M(2,15)$.

Step2: Solve for x - coordinate of U

We know that $\frac{x_1 + x_2}{2}=x_M$. Substituting $x_1 = 6$, $x_M=2$ into $\frac{6 + x}{2}=2$. Cross - multiply: $6 + x=4$. Then $x=4 - 6=-2$.

Step3: Solve for y - coordinate of U

We know that $\frac{y_1 + y_2}{2}=y_M$. Substituting $y_1 = 12$, $y_M = 15$ into $\frac{12 + y}{2}=15$. Cross - multiply: $12 + y=30$. Then $y=30 - 12 = 18$.

Answer:

$(-2,18)$