MCQ
The points $( - a, - b),\;(a,b),\;({a^2},ab)$are
  • A
    Vertices of an equilateral triangle
  • B
    Vertices of a right angled triangle
  • C
    Vertices of an isosceles triangle
  • Collinear

Answer

Correct option: D.
Collinear
d
(d) ${l_1} = \sqrt {{{(2a)}^2} + {{(2b)}^2}} = 2\sqrt {{a^2} + {b^2}} $

${l_2} = \sqrt {{{({a^2} - a)}^2} + {b^2}{{(a - 1)}^2}} = (a - 1)\,\sqrt {{a^2} + {b^2}} $

${l_3} = \sqrt {{{({a^2} + a)}^2} + {b^2}{{(a + 1)}^2}} = (a + 1)\,\sqrt {{a^2} + {b^2}} $

Now ${l_1} + {l_2} = {l_3}.$ Hence points are collinear.

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