if a, b and c are distinct real numbers. then the points A(a,b), B(b,a) and C(c,c) are collines if
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if a, b and c are distinct real numbers. then the points A(a,b), B(b,a) and C(c,c) are collines if
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Step-by-step explanation:
The points A(a, b), B(b, a), and C(c, c) are collinear if the slope between any two points is the same.
For A and B, the slope is \(\frac{a - b}{b - a} = -1\).
For B and C, the slope is \(\frac{a - c}{b - c} = -1\).
For A and C, the slope is \(\frac{b - c}{a - c} = -1\).
So, the points A(a, b), B(b, a), and C(c, c) are collinear if \(a - b = b - a = b - c\), which simplifies to \(a = c\). Therefore, the points are collinear if and only if \(a = c\).