Question

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 the text alone — I need the coordinates or the diagram (or the slopes) of AB, BC, and AC to decide. Give me those and I’ll check.

How to check yourself:
- Compute slopes m_AB, m_BC, m_AC.
- Two sides are perpendicular iff their slopes are negative reciprocals: m1·m2 = −1. (If one side is vertical (undefined slope) and the other horizontal (slope 0), they’re perpendicular.)
- If any pair of sides that meet at a vertex are perpendicular, the triangle is right (the right angle is at that vertex).

Notes about the answer choices:
- “yes, because BC is perpendicular to AC” would be correct only if m_BC · m_AC = −1 (or one is vertical and the other horizontal).
- “yes, because AB is perpendicular to AC” would be correct only if m_AB · m_AC = −1.
- “no, because none of the slopes … are opposite reciprocals” is correct only if indeed no pair of adjacent sides has slopes that multiply to −1.
- “no, because none of the slopes … are equal” is irrelevant — equal slopes mean sides are parallel, not a test for a right triangle.

If you post the coordinates or the slope values (or upload the diagram), I’ll determine which choice is correct.