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On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 3), point B is at (negative 5, negative 1), and point C is at (3, negative 1).
What is true about △ABC? Select three options
AB ⊥ AC
The triangle is a right triangle.
The triangle is an isosceles triangle.
The triangle is an equilateral triangle.
BC ∥ AC
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GPT-5 mini
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Correct options:
- AB ⟂ AC
- The triangle is a right triangle.
- The triangle is an isosceles triangle.
Reason: slope AB = (−1−3)/(−5+1)=−4/−4=1 and slope AC = (−1−3)/(3+1)=−4/4=−1, so AB ⟂ AC (product −1). AB and AC have equal lengths: AB^2 = (−4)^2+(−4)^2=32 and AC^2 = 4^2+(−4)^2=32, so AB = AC (isosceles). Since two sides are perpendicular, the triangle is right.
- AB ⟂ AC
- The triangle is a right triangle.
- The triangle is an isosceles triangle.
Reason: slope AB = (−1−3)/(−5+1)=−4/−4=1 and slope AC = (−1−3)/(3+1)=−4/4=−1, so AB ⟂ AC (product −1). AB and AC have equal lengths: AB^2 = (−4)^2+(−4)^2=32 and AC^2 = 4^2+(−4)^2=32, so AB = AC (isosceles). Since two sides are perpendicular, the triangle is right.
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