Question

Determining If a Triangle Is a Right Triangle

Is triangle ABC a right triangle?

no, because none of the slopes of the line segments forming the legs are opposite reciprocals
no, because none of the slopes of the line segments forming the legs are equal
yes, because BC is perpendicular to AC
yes, because AB is perpendicular to AC

Answer 1

I can’t tell from what you wrote — there’s no diagram or coordinates given. To decide, you need the slopes of AB, BC, and AC (or a picture showing a right angle).

How to check:
- Compute slopes: m_AB = (yB−yA)/(xB−xA), m_BC = (yC−yB)/(xC−xB), m_AC = (yC−yA)/(xC−xA).
- If any pair of side slopes are negative reciprocals (m1 · m2 = −1), those sides are perpendicular and the triangle is right.
- A vertical side and a horizontal side are also perpendicular (undefined slope × 0).

Notes about the answer choices:
- “None of the slopes are opposite reciprocals” means not a right triangle.
- “None of the slopes are equal” just rules out parallel/isosceles — not relevant to rightness.
- “Yes, because BC is perpendicular to AC” or “Yes, because AB is perpendicular to AC” could be correct only if the corresponding slopes are negative reciprocals (or one is vertical and the other horizontal).

If you give the coordinates of A, B, and C (or the diagram), I’ll compute the slopes and tell you which choice is correct.