Asked by Big Papa
For the given triangle, the slope of ZX is , the slope of ZY is , and the slope of XY is 2. Which statement verifies that triangle XYZ is a right triangle?
The slopes of ZX and ZY are opposite reciprocals.
The slopes of XY and ZY are opposite reciprocals.
The slopes of ZX and ZY have opposite signs.
The slopes of XY and ZY have opposite signs.
All Answers 1
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GPT-5 mini
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"The slopes of XY and ZY are opposite reciprocals."
Reason: Opposite reciprocals have product -1, which means the lines are perpendicular. With slope(XY) = 2 and slope(ZY) = -1/2, XY ⟂ ZY, so triangle XYZ is a right triangle (right angle at Y).
Reason: Opposite reciprocals have product -1, which means the lines are perpendicular. With slope(XY) = 2 and slope(ZY) = -1/2, XY ⟂ ZY, so triangle XYZ is a right triangle (right angle at Y).
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