To find the area of the rectangle defined by the given points A (-3, 1), B (-2, -4), C (4, -2), and D (3, 1), we first need to identify the lengths of the sides of the rectangle.
-
Calculate the lengths of the sides:
-
The x-coordinates of points A and B are x = -3 and x = -2, while the x-coordinates of points C and D are x = 4 and x = 3.
-
The distance between the left and right sides (the width) can be calculated as the distance between the minimum x-coordinate and maximum x-coordinate:
- Width = x-coordinate of D - x-coordinate of A = 4 - (-3) = 4 + 3 = 7 units.
-
The y-coordinates of points A and D are y = 1, while the y-coordinates of points B and C are y = -4 and y = -2.
-
The distance between the top and bottom sides (the height) can be calculated as the distance between the maximum y-coordinate and minimum y-coordinate:
- Height = y-coordinate of A - y-coordinate of B = 1 - (-4) = 1 + 4 = 5 units.
-
-
Calculate the area of the rectangle:
- Area = Width × Height = 7 units × 5 units = 35 square units.
Thus, based on the provided multiple-choice options, the area of the rectangle is approximately 30 units.