Q:

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

Accepted Solution

A:
Answer:The fourth coordinate ⇒ (7 , 2)Area of the rectangle ⇒ 45 units²Step-by-step 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