Question

the midpoint m of (overline{tu}) has coordinates (7, 55). point t has coordinates (0, 28). find the coordinates of point u. write the coordinates as decimals or integers. u = ( )

Explanation:

Step1: Recall mid - point formula

The mid - point formula between 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 the coordinates of point $U$ be $(x,y)$, point $T(0,28)$ and mid - point $M(7,55)$.

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

We know that $\frac{0 + x}{2}=7$. Multiply both sides by 2: $0 + x=14$, so $x = 14$.

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

We know that $\frac{28 + y}{2}=55$. Multiply both sides by 2: $28 + y = 110$. Then subtract 28 from both sides: $y=110 - 28=82$.

Answer:

$(14,82)$