if the points A(1,2) B(0,0) and C(a,b) are collinear then what is the relation between a and b ?
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Given,Points A,B and C are collinear Area of ABC = 0 We know that,Area of a triangle formed by (x1,y1) , (x2,y2) and (x3,y3) is given by,Area = 12[x1(y2 ..
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Points A,B and C are collinear
∴ Area of △ABC=0
We know that,
Area of a triangle formed by (x1,y1), (x2,y2) and (x3,y3) is given by,
Area =21[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]
∴ Area of △ABC=21[1(0−b)+0(b−2)+a(2−0)]
⇒0=21[1(0−b)+0(b−2)+a(2−0)]
⇒0=−b+0+2a
⇒2a−b=0
Hence, the relation between a and b is 2a−b=0.