If a b c, prove that the points (a, a2), (b, b2) and (c, c2) can never be collinear.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

If the area of the triangle formed by joining the given points is zero, then the points will be collinear.

Here, x1 = a, y1 = a2; x2 = b, y2 = b2; x3 = c, y3 = c2

Substituting the values in the formula, we get,

Area of triangle =

= [ab2 - ac2 + bc2 - a2b + a2c - cb2]

= [-a2 (b - c) + a (b2 - c2) - bc (b - c)]

= [(b - c) {-a2 + a (b + c) - bc}]

= [(b - c) (-a2 + ab + ac - bc)]

= [(b - c) {a(-a + b) + c(a - b)]

= [(b - c) (a - b) (c - a)]

It is given that a b c, therefore, area of the triangle 0

Hence, the given points can never be collinear.

Answered by  | 4th Jun, 2014, 03:23: PM