Use the coordinates to compute the approximate area of the rectangle.

Point a (-3,1)
Points B (-2,-4)
Point C(4,-2)
Point D (3,1)

(1 point)
• 20 units?
30 units?
© 10 units?
• 40 units=

1 answer

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.

  1. 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.
  2. 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.