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Question
If the points (0,4),(4,0) and (6,2P) are collinear, then the value of P is
If the points (0,4),(4,0) and (6,2P) are collinear, then the value of P is
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Solution
The correct option is A −1
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)=(0,4) ; (x2,y2)=(4,0) and (x3,y3)=(6,2P)
In the area formula, we get
∣∣∣0(0−2P)+4(2P−4)+6(4−0)2∣∣∣=0
⇒8P−16+24=0
⇒8P=−8
⇒P=−1
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)=(0,4) ; (x2,y2)=(4,0) and (x3,y3)=(6,2P)
In the area formula, we get
∣∣∣0(0−2P)+4(2P−4)+6(4−0)2∣∣∣=0
⇒8P−16+24=0
⇒8P=−8
⇒P=−1
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