Question

gh has a mid - point at m(17.15, 13.35). point g is at (18.6, 18.9). 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 $G(x_1,y_1)=(18.6,18.9)$ and $H(x_2,y_2)$. The mid - point $M(17.15,13.35)$.

Step2: Solve for x - coordinate of H

We know that $\frac{x_1 + x_2}{2}=17.15$. Substitute $x_1 = 18.6$ into the equation: $\frac{18.6+x_2}{2}=17.15$. Multiply both sides by 2: $18.6 + x_2=34.3$. Then subtract 18.6 from both sides: $x_2=34.3−18.6 = 15.7$.

Step3: Solve for y - coordinate of H

We know that $\frac{y_1 + y_2}{2}=13.35$. Substitute $y_1 = 18.9$ into the equation: $\frac{18.9+y_2}{2}=13.35$. Multiply both sides by 2: $18.9 + y_2=26.7$. Then subtract 18.9 from both sides: $y_2=26.7−18.9 = 7.8$.

Answer:

$(15.7,7.8)$