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Question
If the points A(1,2), O(0,0) and C(a,b) are collinear then
If the points A(1,2), O(0,0) and C(a,b) are collinear then
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Solution
The correct option is C 2a=b
Since the given points are collinear, they do not form a triangle, which means
area of the triangle is Zero.
Area of a triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is ∣∣∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)2∣∣∣
Hence, substituting the points (x1,y1)=(1,2) ; (x2,y2)=(0,0) and (x3,y3)=(a,b)
in the area formula, we get
∣∣∣1(0−b)+0(a−1)+a(2−02∣∣∣=0
=>−b+2a=0
=>2a=b
Since the given points are collinear, they do not form a triangle, which means
area of the triangle is Zero.
Area of a triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is ∣∣∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)2∣∣∣
Hence, substituting the points (x1,y1)=(1,2) ; (x2,y2)=(0,0) and (x3,y3)=(a,b)
in the area formula, we get
∣∣∣1(0−b)+0(a−1)+a(2−02∣∣∣=0
=>−b+2a=0
=>2a=b
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