Question

Quadrilateral ABCD is a rectangle. The coordinates of A are (x1, y1), and the coordinates of B are (x2, y2). Find the slopes of sides AB, BC, CD, and DA.

1) Cannot be determined
2) A
3) B
4) C

Answer 1

The slopes of horizontal sides AB and CD in a rectangle are 0, while the slopes of vertical sides BC and DA are undefined due to their vertical nature.

Step-by-step explanation:

The question asks us to find the slopes of the sides of a rectangle given two coordinates. For sides AB and CD, which are horizontal, the slope is 0 because they don't rise or fall as they run horizontally. For sides BC and DA, which are vertical, the slope is undefined because there is no run; they rise or fall indefinitely without traveling horizontally.

In a rectangle, opposite sides are parallel and congruent. Let's find the slopes of the sides AB, BC, CD, and DA in terms of the given coordinates.

The slope of AB can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) = coordinates of A and (x2, y2) = coordinates of B.

The slope of BC and DA will be 0 because they are horizontal lines.

The slope of CD will be infinite because it is a vertical line.