Question

A segment has endpoints L(22,7) and K(5, 23). What are the coordinates of the midpoint of LK?

a) (13.5, 15)
b) (17, 15)
c) (13, 15.5)
d) (17, 15.5)

Answer 1

To find the midpoint of a line segment with endpoints L(22,7) and K(5, 23), we use the midpoint formula. Calculating the average of the x-coordinates and y-coordinates separately, we determine that the midpoint coordinates are (13.5, 15).

Step-by-step explanation:

The subject of the question is to find the coordinates of the midpoint of a line segment with given endpoints. To do this, we use the midpoint formula which states that the midpoint, M, with coordinates (xm, ym), of a segment with endpoints L(x1, y1) and K(x2, y2) is calculated as follows:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Applying the formula to our points L(22,7) and K(5, 23), we get:

M = ((22 + 5) / 2, (7 + 23) / 2)

M = (27 / 2, 30 / 2)

M = (13.5, 15)

Therefore, the coordinates of the midpoint are (13.5, 15), which corresponds to option (a).