Geometry. For the floor plans given in exercise 27, determine whether the side through the points (2,3) and (11,6) is perpendicular to the side through the points (2,3) and (-3,18).
# 27 states the following: Geometry. Floor plans for a building have the four corners of a room located at the points (2,3), (11,6), (-3,18), and (8,21). Determine whether the side through the points (2,3) and (11,6) is parallel to the side through the points (-3,18) and (8,21).
determine whether the side
through the points (2, 3) and (11, 6) is perpendicular to the side through the points(2, 3) and (_3, 18).
To determine whether the side through the points (2,3) and (11,6) is perpendicular to the side through the points (2,3) and (-3,18), we need to find the slopes of both lines and check if the slopes are negative reciprocals of each other.
1) Find the slope of the line through (2,3) and (11,6):
Slope = (y2 - y1) / (x2 - x1)
Slope = (6 - 3) / (11 - 2)
Slope = 3 / 9 = 1/3
2) Find the slope of the line through (2,3) and (-3,18):
Slope = (y2 - y1) / (x2 - x1)
Slope = (18 - 3) / (-3 - 2)
Slope = 15 / -5 = -3
Since the slope of the first line is 1/3 and the slope of the second line is -3, they are not negative reciprocals of each other. Therefore, the side through the points (2,3) and (11,6) is not perpendicular to the side through the points (2,3) and (-3,18).