Question

the midpoint m of (overline{tu}) has coordinates (-17.5, 12). point t has coordinates (42, 30). find the coordinates of point 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 the coordinates of $U$ be $(x,y)$, $T=(42,30)$ and $M=(-17.5,12)$.

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

We know that $\frac{42 + x}{2}=-17.5$. Multiply both sides by 2: $42 + x=-17.5\times2=-35$. Then subtract 42 from both sides: $x=-35 - 42=-77$.

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

We know that $\frac{30 + y}{2}=12$. Multiply both sides by 2: $30 + y = 12\times2 = 24$. Then subtract 30 from both sides: $y=24 - 30=-6$.

Answer:

$(-77,-6)$