SOLUTION: 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

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Question 42110This question is from textbook Begining Algebra
: 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 perpendicular to the side through the points (2,3) and (-3,18). This question is from textbook Begining Algebra

Found 2 solutions by psbhowmick, tutorcecilia:
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
Let the points A, B, C and D be represented by the coordinates (2,3), (11,6), (-3,18) and (8,21) respectively.

We are to find whether AB and AC are perpendicular to each other.

Slope of AB = %286-3%29%2F%2811-2%29 = 3%2F9 = 1%2F3.
Slope of AC = %2818-3%29%2F%28-3-2%29 = -15%2F5 = -3.
So the product of the slopes of AB and AC is %281%2F3%29%28-3%29 = -1.
Hence AB and AC are perpendicular to each other.

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
The slopes are perpendicular if their slopes are negative reciprocals of each other.
.
For example: m1 is perpendicular to m2 because m1 = 2/1 and m2 = -(1/2).
.
First, find the slope of each set of coordinate points.
The formula for slope is:
delta y/delta x = (y1-y2)/(x1-x2):
The slope m1 of (2,3) and (11,6) = (3-6)/(2-11) = -3/-9 = 1/3
.
The slope of m2 of (2,3) and (-3,18) = (3-18)/2-(-3)= -15/5 = -3/1
.
The slopes are the negative reciprocals of each other:
1/3 is the negative reciprocal of -3/1.
Therefore, the lines are perpendicular.