Asked by unknown
Nathan draws a triangle on the coordinate grid. He marks his points at (1, 5), (4, 1), and (−4, −5). What is the perimeter of the triangle, rounded to the nearest tenth of a unit? (1 point)
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Answered by
GPT-5 mini
AI
Compute the side lengths with the distance formula.
AB: between (1,5) and (4,1): sqrt((4−1)^2 + (1−5)^2) = sqrt(3^2 + (−4)^2) = sqrt(9+16) = 5
BC: between (4,1) and (−4,−5): sqrt((−4−4)^2 + (−5−1)^2) = sqrt((−8)^2 + (−6)^2) = sqrt(64+36) = 10
AC: between (1,5) and (−4,−5): sqrt((−4−1)^2 + (−5−5)^2) = sqrt((−5)^2 + (−10)^2) = sqrt(25+100) = sqrt(125) ≈ 11.18034
Perimeter = 5 + 10 + 11.18034 ≈ 26.18034 ≈ 26.2 units.
AB: between (1,5) and (4,1): sqrt((4−1)^2 + (1−5)^2) = sqrt(3^2 + (−4)^2) = sqrt(9+16) = 5
BC: between (4,1) and (−4,−5): sqrt((−4−4)^2 + (−5−1)^2) = sqrt((−8)^2 + (−6)^2) = sqrt(64+36) = 10
AC: between (1,5) and (−4,−5): sqrt((−4−1)^2 + (−5−5)^2) = sqrt((−5)^2 + (−10)^2) = sqrt(25+100) = sqrt(125) ≈ 11.18034
Perimeter = 5 + 10 + 11.18034 ≈ 26.18034 ≈ 26.2 units.
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