Question

the midpoint m of (overline{tu}) has coordinates (-43.5, 19). point u has coordinates (-66, -11). find the coordinates of point t. write the coordinates as decimals or integers. t = (, )

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 point $T$ be $(x,y)$ and of point $U$ be $(-66,-11)$ and of mid - point $M$ be $(-43.5,19)$.

Step2: Solve for $x$

We know that $\frac{x+( - 66)}{2}=-43.5$. Multiply both sides by 2: $x-66=-43.5\times2=-87$. Then add 66 to both sides: $x=-87 + 66=-21$.

Step3: Solve for $y$

We know that $\frac{y+( - 11)}{2}=19$. Multiply both sides by 2: $y-11=19\times2 = 38$. Then add 11 to both sides: $y=38 + 11=49$.

Answer:

$(-21,49)$