Question

Use the coordinates to compute the approximate area of the rectangle.
A (-3,-1)
B (-2,-4)
C (4,-2)
D (3,1)
(1 point)
Responses

30 units2
30 units squared

40 units2
40 units squared

20 units2
20 units squared

10 units2

Answer 1

To compute the approximate area of the rectangle, we can use the distance formula to find the length and width of the rectangle.

The distance between points A (-3,-1) and B (-2,-4) is:
√((-2 - (-3))^2 + (-4 - (-1))^2) = √(1^2 + (-3)^2) = √(1 + 9) = √10

The distance between points B (-2,-4) and C (4,-2) is:
√((4 - (-2))^2 + (-2 - (-4))^2) = √(6^2 + 2^2) = √(36 + 4) = √40

The length of the rectangle is √10 and the width is √40.

To find the area, we multiply the length by the width:
√10 * √40 = √(10*40) = √400 = 20

Therefore, the approximate area of the rectangle is 20 units2.