Asked by Sam
Janet draws triangle PQR with vertices P(1,), Q(-2,4), and R(1,7) she claims that the triangle is an isosceles right triangle which statement shows that Janet is correct the slope of PQ is 1 which is the reciprocal of the slope of QR and PQ and QR are equal to 6 the slope of PQ is 1 which is the reciprocal of the slope of QR and PQ are equal to 3 2 the slope is -1 which is the negative reciprocal of the slope QR and PQ and QR are equal to 6 or the slope of PQ is -1 which is the negative reciprocal of the slope of QR and PQ and QR are equal to 3 2
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GPT-5 mini
AI
Compute slopes and lengths.
Slope QR = (7 − 4)/(1 − (−2)) = 3/3 = 1.
If P = (1,1) then slope PQ = (1 − 4)/(1 − (−2)) = −3/3 = −1, which is the negative reciprocal of 1, so PQ ⟂ QR.
Length QR = sqrt[(1 − (−2))^2 + (7 − 4)^2] = sqrt(9 + 9) = 3√2.
Length PQ = sqrt[(1 − (−2))^2 + (1 − 4)^2] = sqrt(9 + 9) = 3√2.
Thus PQ ⟂ QR and PQ = QR = 3√2, so the triangle is an isosceles right triangle. The correct statement is: "the slope of PQ is −1 which is the negative reciprocal of the slope of QR and PQ and QR are equal to 3√2."
Slope QR = (7 − 4)/(1 − (−2)) = 3/3 = 1.
If P = (1,1) then slope PQ = (1 − 4)/(1 − (−2)) = −3/3 = −1, which is the negative reciprocal of 1, so PQ ⟂ QR.
Length QR = sqrt[(1 − (−2))^2 + (7 − 4)^2] = sqrt(9 + 9) = 3√2.
Length PQ = sqrt[(1 − (−2))^2 + (1 − 4)^2] = sqrt(9 + 9) = 3√2.
Thus PQ ⟂ QR and PQ = QR = 3√2, so the triangle is an isosceles right triangle. The correct statement is: "the slope of PQ is −1 which is the negative reciprocal of the slope of QR and PQ and QR are equal to 3√2."
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