Question

gh has a mid - point at m(5.5, 15.5). point g is at (9, 19). 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 $G(x_1,y_1)=(9,19)$ and $H(x_2,y_2)$. The mid - point $M(5.5,15.5)$.

Step2: Solve for the x - coordinate of H

We know that $\frac{x_1 + x_2}{2}=5.5$. Substitute $x_1 = 9$ into the equation: $\frac{9 + x_2}{2}=5.5$. Multiply both sides by 2: $9+x_2 = 11$. Then subtract 9 from both sides: $x_2=11 - 9=2$.

Step3: Solve for the y - coordinate of H

We know that $\frac{y_1 + y_2}{2}=15.5$. Substitute $y_1 = 19$ into the equation: $\frac{19 + y_2}{2}=15.5$. Multiply both sides by 2: $19+y_2 = 31$. Then subtract 19 from both sides: $y_2=31 - 19 = 12$.

Answer:

$(2,12)$