Question

the midpoint m of tu has coordinates (-1, 7). point t has coordinates (6, 7). 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 point $T=(x_T,y_T)=(6,7)$ and the coordinates of point $U=(x_U,y_U)$, and the mid - point $M=(-1,7)$.

Step2: Solve for the x - coordinate of U

We know that $\frac{x_T+x_U}{2}=x_M$. Substitute $x_T = 6$ and $x_M=-1$ into the formula: $\frac{6 + x_U}{2}=-1$. Multiply both sides by 2: $6 + x_U=-2$. Then subtract 6 from both sides: $x_U=-2 - 6=-8$.

Step3: Solve for the y - coordinate of U

We know that $\frac{y_T+y_U}{2}=y_M$. Substitute $y_T = 7$ and $y_M = 7$ into the formula: $\frac{7 + y_U}{2}=7$. Multiply both sides by 2: $7 + y_U=14$. Subtract 7 from both sides: $y_U=7$.

Answer:

$(-8,7)$