Question

what is the midpoint of the segment joining the points (2, 3) and (6, 7)?
(4, 5)
(6, 3)
(8, 10)
(2, 7)

Explanation:

Step1: Recall midpoint formula

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

Step2: Substitute x-values

Plug $x_1=2, x_2=6$ into x-midpoint formula:
$$x_m = \frac{2+6}{2} = \frac{8}{2} = 4$$

Step3: Substitute y-values

Plug $y_1=3, y_2=7$ into y-midpoint formula:
$$y_m = \frac{3+7}{2} = \frac{10}{2} = 5$$

Answer:

(4, 5)