CBSE Class 10 Answered
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.