For the floor plans given in exercise27, 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).

Compute the slopes of the two lines. If the product of the slopes is -1, then te lines are perpendicular.

In your case, the first line has a slope of m = (6-3)/(11-2)= 1/3 and the second line has a slope of
m = (18-3)/(-3 -2) = 15/(-5) = ?

You finish it.

You could also do the problem graphically by plotting the points, drawing the lines and using a protractor.

To determine whether the two lines are perpendicular, we need to compute their slopes and check if their product is -1. The slope of a line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

Let's calculate the slope of the line passing through points (2, 3) and (11, 6):

m1 = (6 - 3) / (11 - 2) = 3 / 9 = 1/3

Next, we need to calculate the slope of the line passing through points (2, 3) and (-3, 18):

m2 = (18 - 3) / (-3 - 2) = 15 / -5 = -3

Now, we can check if the product of the slopes is -1:

m1 * m2 = (1/3) * (-3) = -1

Since the product of the slopes is -1, we can conclude that the line passing through the points (2, 3) and (11, 6) is perpendicular to the line passing through the points (2, 3) and (-3, 18).

Alternatively, you can solve this problem graphically by plotting the points on a coordinate plane, drawing the lines, and using a protractor to measure the angles formed by the lines. If the angles measure 90 degrees, the lines are perpendicular.