The vertices of a triangle are A(2, 1), B(8, 1) and C(5, 5). Work out all three side lengths and decide which description of triangle ABC is correct.

Question

Accepted Answer

Isosceles: CA = CB = 5 while AB = 6. AB = |8 - 2| = 6. CB = √(8-5)^2 + (1-5)^2 = √9+16 = 5 and CA = √(5-2)^2 + (5-1)^2 = √9+16 = 5. Exactly two sides are equal, so ABC is isosceles. It is not right-angled: CA^2 + CB^2 = 25 + 25 = 50, which is not AB^2 = 36. Calling it scalene comes from mis-subtracting one of the pairs.

The vertices of a triangle are A(2, 1), B(8, 1) and C(5, 5). Work out all three side lengths and decide which description of triangle ABC is correct.

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