Question

the midpoint of tu is m(15, 14.5). one endpoint is t(14, 20). 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 $T(x_1,y_1)=(14,20)$ and $U(x_2,y_2)$, and $M(15,14.5)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=15$. Substitute $x_1 = 14$ into the equation: $\frac{14+x_2}{2}=15$. Multiply both sides by 2: $14 + x_2=30$. Then subtract 14 from both sides: $x_2=30 - 14=16$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=14.5$. Substitute $y_1 = 20$ into the equation: $\frac{20 + y_2}{2}=14.5$. Multiply both sides by 2: $20+y_2 = 29$. Then subtract 20 from both sides: $y_2=29 - 20 = 9$.

Answer:

$(16,9)$