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Question
If the points (5,1), (1,p) & (4,2) are collinear then the value of p will be
If the points (5,1), (1,p) & (4,2) are collinear then the value of p will be
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Solution
The correct option is B 5
Area of a triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is ∣∣∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)2∣∣∣
Since the given points are collinear, they do not form a triangle, which means area of the triangle is Zero.
Hence, substituting the points (x1,y1)=(5,1) ; (x2,y2)=(1,P) and (x3,y3)=(4,2) in the area formula, we get ∣∣∣5(P−2)+1(2−1)+4(1−P)2∣∣∣=0
=>5P−10+1+4−4P=0
=>P=5
Area of a triangle with vertices (x1,y1) ; (x2,y2) and (x3,y3) is ∣∣∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)2∣∣∣
Since the given points are collinear, they do not form a triangle, which means area of the triangle is Zero.
Hence, substituting the points (x1,y1)=(5,1) ; (x2,y2)=(1,P) and (x3,y3)=(4,2) in the area formula, we get ∣∣∣5(P−2)+1(2−1)+4(1−P)2∣∣∣=0
=>5P−10+1+4−4P=0
=>P=5
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