Question

14. If the points P(1, 2), B(0, 0) and C(a, b) are collinear, then prove that 2a=b.​

Answer 1

Answer:

$Since the given points are collinear, they do not form a triangle, which means</p><p>area of the triangle is Zero. </p><p>Area of a triangle with vertices (x1,y1) ; (x2,y2)  and (x3,y3)  is ∣∣∣∣∣2x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣∣∣∣∣</p><p>Hence, substituting the points (x1,y1)=(1,2) ; (x2,y2)=(0,0)  and (x3,y3)=(a,b)</p><p>in the area formula, we get</p><p>∣∣∣∣∣21(0−b)+0(a−1)+a(2−0∣∣∣∣∣=0</p><p>=>−b+2a=0</p><p>=>2a=b</p><p></p><p>$

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