Question

The points (0, 8/3) (1, 3) and (82, 30) are the vertices of

• A. An equilateral triangle
• B. An isosceles triangle
• C. A right angled triangle
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Here $A = (0,8/3),B = (1,3)\text{and }C = (82,30)$

$AB = \sqrt{1 + 1/9} = \sqrt{10/9}$, $BC = \sqrt{(81)^{2} + (27)^{2}} = 27\sqrt{10}$=

$81\sqrt{\frac{10}{9}}$, $AC = \sqrt{(82)^{2} + (30 - 8/3)^{2}} = 82\sqrt{\frac{10}{9}}$

Since $AB + BC = (1 + 81)\sqrt{\frac{10}{9}} = 82\sqrt{\frac{10}{9}} = AC$.

∴ Points A, B, C are collinear