Question

point j(5, -9) is the midpoint of $overline{hi}$. if h is located at (2, -6), what are the coordinates of i? write your answers as integers or decimals. ( , )

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Let $H(x_1,y_1)=(2,-6)$ and $I(x_2,y_2)$, and the mid - point $J(5,-9)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=5$. Substitute $x_1 = 2$ into the equation: $\frac{2+x_2}{2}=5$. Multiply both sides by 2: $2 + x_2=10$. Then subtract 2 from both sides: $x_2=10 - 2=8$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=-9$. Substitute $y_1=-6$ into the equation: $\frac{-6 + y_2}{2}=-9$. Multiply both sides by 2: $-6 + y_2=-18$. Then add 6 to both sides: $y_2=-18 + 6=-12$.

Answer:

$(8,-12)$