Question

1. the coordinates of the midpoint of gh are m (-2, 5) and the coordinates of one endpoint are h (-3, 7). find the coordinates of the other endpoint. the coordinates of the other endpoint are ( , )

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 the coordinates of the mid - point $M$ be $(-2,5)$ and one endpoint $H(x_1,y_1)=(-3,7)$. Let the other endpoint be $G(x_2,y_2)$.

Step2: Solve for $x_2$

We know that $\frac{x_1 + x_2}{2}=-2$. Substitute $x_1=-3$ into the equation: $\frac{-3 + x_2}{2}=-2$. Multiply both sides by 2: $-3 + x_2=-4$. Add 3 to both sides: $x_2=-4 + 3=-1$.

Step3: Solve for $y_2$

We know that $\frac{y_1 + y_2}{2}=5$. Substitute $y_1 = 7$ into the equation: $\frac{7 + y_2}{2}=5$. Multiply both sides by 2: $7 + y_2 = 10$. Subtract 7 from both sides: $y_2=10 - 7 = 3$.

Answer:

$(-1,3)$