Find the type of triangle ABC formed whose vertices are $A(1, 0)$, $B(-5, 0)$ and $C(-2, 5)$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer
Using the distance formula:
$$AB = \sqrt{(-5-1)^2 + (0-0)^2} = \sqrt{36} = 6$$
$$BC = \sqrt{(-2+5)^2 + (5-0)^2} = \sqrt{9+25} = \sqrt{34}$$
$$CA = \sqrt{(1+2)^2 + (0-5)^2} = \sqrt{9+25} = \sqrt{34}$$
Since $BC = CA = \sqrt{34}$ but $AB = 6 \neq \sqrt{34}$, triangle ABC is an isosceles triangle.
Source: Chapter 7, Section 7.2 (Distance Formula)
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Explanation
- The examiner wants you to calculate all three sides using the distance formula and then compare them.
- If two sides are equal → isosceles; all three equal → equilateral; none equal → scalene; check Pythagoras for right-angled.
- Always state the conclusion clearly. One mark is typically for correct calculation; the second for the correct identification of triangle type.