Question

The coordinates below are the three vertices of a rectangle. Identify the fourth coordinate and the area of the rectangle. A coordinate plane with the following points A at negative 2, 2; B at negative 2, negative 3; and C at 7, negative 3. (4 points) (2, 7), 28 units squared (2, 7), 45 units squared (7, 2), 28 units squared (7, 2), 45 units squared

Answer 1

The answer is: (7,2), 45 units.

I took the quiz and I got it right! :)

Answer 2

The fourth coordinate ⇒ (7 , 2)

Area of the rectangle ⇒ 45 units²

Explanation:

∵ A (-2 , 2) , B (-2 , -3) , C (7 , -3)

∵ ABCD is a rectangle

∵ AC bisects BD

∴ xD = xA + xC - xB

∴ xD = -2 + 7 - (-2) = -2 + 7 + 2 = 7

∴ yD = yA + yC - yB

∴ yD = 2 + (-3) - (-3) = 2 - 3 + 2 = 2

∴ Point D is (7 , 2)

∵ AB is a vertical segment (same x-coordinates)

∴ AB = 2 - (-3) = 2 + 3 = 5 units

∵ BC is a horizontal segment (same y-coordinates)

∴ BC = 7 - (-2) = 7 + 2 = 9 units

∵ Area rectangle = base × height

∴ Area = 9 × 5 = 45 units²