Question

8. Show that the points (2, -2), (-2, 1) and (5, 2) are the vertices of a right angled
triangle.
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Answer 1

Name three vertices (2, -2), (-2, 1) and (5, 2).

• A(2, -2)
• B(-2, 1)
• C(5, 2)

According to the distance formula

$\sf{\overline{AB}^2=(2+2)^2+(-2-1)^2}$

→ $\sf{\overline{AB}^2=25}$

$\sf{\overline{BC}^2=(-2-5)^2+(1-2)^2}$

→ $\sf{\overline{BC}^2=50}$

$\sf{\overline{CA}^2=(5-2)^2+(2+2)^2}$

→ $\sf{\overline{CA}^2=25}$

Now it is clear that $\sf{\overline{AB}^2+\overline{CA}^2=\overline{BC}^2}$.

The Pythagorean theorem states it right-angled at ∠A.