Question

The perimeter of the quadrilateral ABCD formed by A(-3, 1), B(0, 5), C(4, 8), D(1, 4) taken in that order is

• A. \(16\sqrt{2}\)
• B. 25
• C. 20
• D. 10

Answer 1

The Correct Option is C

To find the perimeter of the quadrilateral, we need to calculate the distance between each consecutive pair of points, and then sum the distances. 1. The distance between points A(-3, 1) and B(0, 5): \[ d_{AB} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(0 - (-3))^2 + (5 - 1)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] 2. The distance between points B(0, 5) and C(4, 8): \[ d_{BC} = \sqrt{(4 - 0)^2 + (8 - 5)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \] 3. The distance between points C(4, 8) and D(1, 4): \[ d_{CD} = \sqrt{(1 - 4)^2 + (4 - 8)^2} = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] 4. The distance between points D(1, 4) and A(-3, 1): \[ d_{DA} = \sqrt{(1 - (-3))^2 + (4 - 1)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \] Now, the perimeter is the sum of these distances: \[ \text{Perimeter} = d_{AB} + d_{BC} + d_{CD} + d_{DA} = 5 + 5 + 5 + 5 = 20 \]

The correct option is (C): 20