Question

gh has a midpoint at m(-13.5, -5). point g is at (-16, -12). find the coordinates of point h. write the coordinates as decimals or integers. h = ( )

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 $G(x_1,y_1)=(-16,-12)$ and $H(x_2,y_2)$. The mid - point $M(x_m,y_m)=(-13.5,-5)$.

Step2: Solve for the x - coordinate of H

We know that $x_m=\frac{x_1 + x_2}{2}$. Substituting the values, we have $-13.5=\frac{-16 + x_2}{2}$. Multiply both sides by 2: $-13.5\times2=-16 + x_2$. So, $-27=-16 + x_2$. Then add 16 to both sides: $x_2=-27 + 16=-11$.

Step3: Solve for the y - coordinate of H

We know that $y_m=\frac{y_1 + y_2}{2}$. Substituting the values, we have $-5=\frac{-12 + y_2}{2}$. Multiply both sides by 2: $-5\times2=-12 + y_2$. So, $-10=-12 + y_2$. Then add 12 to both sides: $y_2=-10 + 12 = 2$.

Answer:

$(-11,2)$