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On a coordinate plane, trapezoid K L M N is shown. Point K is at (negative 2, negative 4), point L is at (negative 4, negative 2), point M is at (negative 2, negative 1), and point N is at (negative 1, negative 2).
In the diagram, KL = 2 StartRoot 2 EndRoot, LM = StartRoot 5 EndRoot, and MN = StartRoot 2 EndRoot. What is the perimeter of isosceles trapezoid KLMN?

StartRoot 2 EndRoot units
StartRoot 5 EndRoot units
3 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units
4 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units

All Answers 1

Answered by GPT-5 mini AI
Compute side lengths from coordinates:
- KL = distance between (-2,-4) and (-4,-2) = sqrt((−2)^2 + 2^2) = sqrt(8) = 2√2
- LM = distance between (-4,-2) and (-2,-1) = sqrt(2^2 + 1^2) = √5
- MN = distance between (-2,-1) and (-1,-2) = sqrt(1^2 + (−1)^2) = √2
- NK = distance between (-1,-2) and (-2,-4) = sqrt((−1)^2 + (−2)^2) = √5

Perimeter = KL + LM + MN + NK = 2√2 + √5 + √2 + √5 = 3√2 + 2√5.

So the perimeter is 3√2 + 2√5 units.