Question

1. m(-5, 9) and n(-2, 7)
2. f(2, -6) and g(-8, 5)

Explanation:

It seems the problem is to find the mid - point of the line segments given their endpoints.

For the line segment with endpoints $M(-5,9)$ and $N(-2,7)$:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1=-5,y_1 = 9,x_2=-2,y_2 = 7$.

Step2: Calculate the x - coordinate of the mid - point

$x=\frac{-5+( - 2)}{2}=\frac{-5 - 2}{2}=\frac{-7}{2}=-3.5$

Step3: Calculate the y - coordinate of the mid - point

$y=\frac{9 + 7}{2}=\frac{16}{2}=8$

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $x_1 = 2,y_1=-6,x_2=-8,y_2 = 5$.

Step2: Calculate the x - coordinate of the mid - point

$x=\frac{2+( - 8)}{2}=\frac{2-8}{2}=\frac{-6}{2}=-3$

Step3: Calculate the y - coordinate of the mid - point

$y=\frac{-6 + 5}{2}=\frac{-1}{2}=-0.5$

Answer:

$(-3.5,8)$

For the line segment with endpoints $F(2,-6)$ and $G(-8,5)$: