Question

tu has a mid - point at m(6, 27). point t is at (17, 29). 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 $T(x_1,y_1)=(17,29)$ and $U(x_2,y_2)$. The mid - point $M(6,27)$.

Step2: Find the x - coordinate of U

We know that $\frac{x_1 + x_2}{2}=6$. Substitute $x_1 = 17$ into the equation: $\frac{17+x_2}{2}=6$. Multiply both sides by 2: $17 + x_2=12$. Then solve for $x_2$: $x_2=12 - 17=-5$.

Step3: Find the y - coordinate of U

We know that $\frac{y_1 + y_2}{2}=27$. Substitute $y_1 = 29$ into the equation: $\frac{29+y_2}{2}=27$. Multiply both sides by 2: $29 + y_2 = 54$. Then solve for $y_2$: $y_2=54 - 29 = 25$.

Answer:

$(-5,25)$