Question

Find the ratio in which the perpendicular from (1,5) to the line segment joining (1,1) and (5,5) divides the segment.

a) 1:1
b) 1:2
c) 2:1
d) 3:1

Answer 1

The perpendicular from point (1,5) divides the line segment joining points (1,1) and (5,5) in a 1:1 ratio because the perpendicular intersects at the midpoint of the segment.

Step-by-step explanation:

To find the ratio in which the perpendicular from (1,5) to the line segment joining (1,1) and (5,5) divides the segment, we should first understand that the line segment has endpoints with the same x and y increments, which means it has a slope of 1. A perpendicular line to this segment would have a slope of -1 (the negative reciprocal). Since the x-coordinate of the point (1,5) and the first endpoint of the segment (1,1) are the same, the perpendicular line to the segment will go through (1,5) and intersect the segment at its midpoint, which is equidistant from both endpoints. Hence, the segment is divided into two equal parts by the perpendicular from (1,5).