Question

Name the quadrilateral formed by plotting the following points. Also, find the perimeter.

C(5, 1), D(−1, 9), E(−5, 6), F(1, −2)

Answer 1

Given:

C(5, 1), D(−1, 9), E(−5, 6), F(1, −2)

The distance between two points (x₁,y₁) and (x₂,y₂) is \[\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

CE: \[ \sqrt{(-1 - 5)^2 + (9 - 1)^2} = \sqrt{(-6)^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10\]

ED: \[\sqrt{(-5 - (-1))^2 + (6 - 9)^2} = \sqrt{(-4)^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5\]

DF: \[\sqrt{(1 - (-5))^2 + (-2 - 6)^2} = \sqrt{6^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10\]

FC: \[\sqrt{(5 - 1)^2 + (1 - (-2))^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5\]

Step 2: Identify the Quadrilateral

Opposite sides are equal:

CD = EF = 10

DE = FC = 5

Adjacent sides are perpendicular. So, the figure is a rectangle.

Step 3: Find the Perimeter

Perimeter = CD + DE + EF + FC

= 10 + 5 + 10 + 5

= 30 units