Question

The midpoint of the segment joining points (a, b) and (j, k) is

a. ( j - a, k - b)
b. (j- a/2, k-b/2)
c. (j+a, k+b)
d. ( j+a/2, k+b/2)

Answer 1

The midpoint of the segment joining points (a, b) and (j, k) is found by averaging the x-coordinates and the y-coordinates of the two endpoints, making the correct answer (j+a/2, k+b/2).

Step-by-step explanation:

The student has asked about finding the midpoint of the segment joining two points in a coordinate plane. The correct answer is that the midpoint, M, of a line segment with endpoints (a, b) and (j, k) can be found using the midpoint formula which is:
M = \(\left(\frac{a + j}{2}, \frac{b + k}{2}\right)\).

This formula takes the average of the x-coordinates and the average of the y-coordinates of the two endpoints to find the center point. Based on this formula, the correct option is:

d. \(\left(\frac{j + a}{2}, \frac{k + b}{2}\right)\)