Question

tu has a midpoint at m(-26, 33). point u is at (-78, 71). 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 $(-78,71)$ and mid - point $M(-26,33)$.

Step2: Solve for the x - coordinate of T

We know that $\frac{x+( - 78)}{2}=-26$. Multiply both sides by 2: $x - 78=-52$. Then add 78 to both sides: $x=-52 + 78=26$.

Step3: Solve for the y - coordinate of T

We know that $\frac{y + 71}{2}=33$. Multiply both sides by 2: $y+71 = 66$. Then subtract 71 from both sides: $y=66 - 71=-5$.

Answer:

$(26,-5)$