Question

Given the points A(-1,2) and B(7,6), find the coordinates of the point P on directed line segment AB that partitions the segment into a ratio 1:

Answer 1

The midpoint of line segment AB with endpoints A(-1,2) and B(7,6) is found using the Midpoint Formula, resulting in point P with coordinates (3, 4) that divides AB into equal parts.

Step-by-step explanation:

The quest is to find the coordinates of the point P on the directed line segment AB that partitions the segment into the ratio 1:1. Since the question specifies a ratio of 1:1, this implies that point P is the midpoint of line segment AB. To determine the midpoint, the following formula is used:

Midpoint Formula: ((x1 + x2) / 2, (y1 + y2) / 2)

Plugging in the coordinates of A(-1,2) and B(7,6), we get:

Midpoint P = ((-1 + 7) / 2, (2 + 6) / 2) = (6 / 2, 8 / 2) = (3, 4)

Therefore, the coordinates of point P that divides the segment AB into equal parts are (3, 4).