Question

Two adjacent vertices of a square are A(2, 3) and B(2, 8). What are the slopes of the lines that form the sides of the square?

A. Two sides have slope 5 and two lines have slope −15.
B. All of the sides have slope 0.
C. Two sides have slope 0 and two sides have undefined slopes.
D. All of the sides have undefined slopes.

Answer 1

The slopes of a square with two adjacent vertices A(2, 3) and B(2, 8) are two sides with slope 0 (horizontal lines) and two sides with undefined slopes (vertical lines).

Step-by-step explanation:

To determine the slopes of the lines that form the sides of the square, we consider two adjacent vertices A(2, 3) and B(2, 8). Since both points A and B have the same x-coordinate but different y-coordinates, this indicates that the line AB is vertical. The slope of a vertical line is undefined. Therefore, the square has two sides that are vertical and thus have undefined slopes.

Now, the sides perpendicular to AB will be horizontal, as they must form right angles with AB to make a square. Horizontal lines have a slope of 0 because there is no rise over the run—the y-coordinate remains constant while the x-coordinate changes. Thus, the square also has two sides that are horizontal with a slope of 0.

The correct answer to the stated problem is, therefore, option C: Two sides have slope 0 and two sides have undefined slopes.