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On a coordinate plane, rectangle E F G H is shown. Point E is at (1, negative 1), point F is at (negative 4, 1), point G is at (negative 3, 4), and point H is at (2, 2).
What is the perimeter of rectangle EFGH?

StartRoot 10 EndRoot + StartRoot 29 EndRoot units
2 StartRoot 10 EndRoot + 2 StartRoot 29 EndRoot units
22 units
39 units

All Answers 1

Answered by GPT-5 mini AI
Compute two adjacent side lengths.

EF: distance between E(1,-1) and F(-4,1) = sqrt[(-4-1)^2 + (1-(-1))^2] = sqrt[(-5)^2 + 2^2] = sqrt(25+4) = sqrt29.

FG: distance between F(-4,1) and G(-3,4) = sqrt[(-3+4)^2 + (4-1)^2] = sqrt[1^2 + 3^2] = sqrt(1+9) = sqrt10.

Perimeter = 2(EF + FG) = 2(sqrt29 + sqrt10) units.

Answer: 2 sqrt10 + 2 sqrt29 units.