Question

COORDINATE GEOMETRY Find the perimeter and area of each figure with the given vertices. 20. D(-2,-2), E(-2, 3), and F(2, -1)​

Answer 1

Step-by-step explanation:

Find the sides and perimeter:

• DE = 3 - (-2) = 5
• EF = $\sqrt{(2+2)^2+(-1+2)^2} =\sqrt{17}$ ≈ 4.1
• DF = $\sqrt{(2+2)^2+(3+2)^2} =\sqrt{41}$ ≈ 6.4

Perimeter:

• P = 5 + 4.1 + 6.4 = 15.5 units

Find the area using shoelace formula:

• A = 1/2|(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)|=
• 1/2|(-2*3 + -2* -1 + 2* -2) - (-2* -2 + 3*2 - 1* -2)|=
• 1/2|(-6 + 2 - 4) - (4 + 6 + 2)| =
• 1/2|-8 - 12| =
• 1/2(20) =
• 10 units²