Question

Use slopes to show that the quadrilateral whose vertices are (-1,0),(2,3),(1,-2), and (4,1) is a rectangle

Answer 1

To show that the quadrilateral is a rectangle, we need to examine the slopes of its sides. If the slopes of the opposite sides are negative reciprocals of each other and the lengths of opposite sides are equal, then the quadrilateral is a rectangle.

Step-by-step explanation:

To show that the quadrilateral is a rectangle, we need to examine the slopes of its sides. If the slopes of the opposite sides are negative reciprocals of each other and the lengths of opposite sides are equal, then the quadrilateral is a rectangle.

1. Calculate the slopes of the four sides using the slope formula, which is (y2-y1)/(x2-x1). The slopes are: -1/3, -1/3, -1/3, -1/3.
2. Since the slopes are all the same and the lengths of opposite sides are equal, we can conclude that the quadrilateral is a rectangle.