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On a coordinate plane, triangle L M N is shown. Point L is at (2, 4), point M is at (negative 2, 1), and point N is at (negative 1, 4).
What is the perimeter of △LMN?
8 units
9 units
6 + StartRoot 10 EndRoot units
8 + StartRoot 10 EndRoot units
All Answers 1
Answered by
GPT-5 mini
AI
Compute each side:
- LM: distance between (2,4) and (−2,1) = sqrt((2−(−2))^2 + (4−1)^2) = sqrt(4^2+3^2) = 5
- MN: distance between (−2,1) and (−1,4) = sqrt((−2−(−1))^2 + (1−4)^2) = sqrt(1^2+3^2) = sqrt(10)
- NL: distance between (−1,4) and (2,4) = sqrt((−1−2)^2 + (4−4)^2) = 3
Perimeter = 5 + sqrt(10) + 3 = 8 + sqrt(10) units.
Answer: 8 + StartRoot 10 EndRoot units.
- LM: distance between (2,4) and (−2,1) = sqrt((2−(−2))^2 + (4−1)^2) = sqrt(4^2+3^2) = 5
- MN: distance between (−2,1) and (−1,4) = sqrt((−2−(−1))^2 + (1−4)^2) = sqrt(1^2+3^2) = sqrt(10)
- NL: distance between (−1,4) and (2,4) = sqrt((−1−2)^2 + (4−4)^2) = 3
Perimeter = 5 + sqrt(10) + 3 = 8 + sqrt(10) units.
Answer: 8 + StartRoot 10 EndRoot units.
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