Question

in the standard $(x, y)$ coordinate plane, what is the midpoint of the line segment that has endpoints $(-6, 9)$ and $(2, 5)$?
a $(-4, -4)$
b $(-2, 7)$
c $(4, -2)$
d $(8, -4)$

Explanation:

Step1: Recall midpoint formula

The midpoint $(M_x, M_y)$ of two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:
$$M_x = \frac{x_1+x_2}{2}, \quad M_y = \frac{y_1+y_2}{2}$$

Step2: Substitute x-values

Let $(x_1,y_1)=(-6,9)$ and $(x_2,y_2)=(2,5)$. Calculate $M_x$:
$$M_x = \frac{-6+2}{2} = \frac{-4}{2} = -2$$

Step3: Substitute y-values

Calculate $M_y$:
$$M_y = \frac{9+5}{2} = \frac{14}{2} = 7$$

Answer:

B. (-2, 7)