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If a≠b≠c,then prove that the points …

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If a≠b≠c,then prove that the points (a,a×a),(b,b×b), (c,c×c) can never be collinear.

Posted by Nikhil Kumar 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let A(a, a²), B(b, b²) and C(c, c²) be the given points.
{tex}\therefore{/tex}Area of {tex}\Delta A B C{/tex}
{tex}= \frac { 1 } { 2 } \left\{ a \left( b ^ { 2 } - c ^ { 2 } \right) + b \left( c ^ { 2 } - a ^ { 2 } \right) + c \left( a ^ { 2 } - b ^ { 2 } \right) \right\}{/tex}
{tex}= \frac { 1 } { 2 } \left\{ a b ^ { 2 } - a c ^ { 2 } + b c ^ { 2 } - b a ^ { 2 } + c a ^ { 2 } - c b ^ { 2 } \right\}{/tex}
{tex}= \frac { 1 } { 2 } \times 0{/tex} [if a = b = c]
=0
i.e., the points are collinear if a = b = c
Hence, the points can never be collinear if {tex}a \neq b \neq c.{/tex}

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