1
Question
If the points(7,−2),(5,1),(3,K)are collinear,then the value of K is :
If the points(7,−2),(5,1),(3,K)are collinear,then the value of K is :
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Solution
The correct option is C 4
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)=(7,−2) ; (x2,y2)=(5,12) and (x3,y3)=(3,k)
in the area formula, we get
∣∣∣7(1−k)+5(k+2)+3(−2−1)2∣∣∣=0
=>7−7k+5k+10−9=0
=>2k=8
=>k=4
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∣∣∣
in the area formula, we get
∣∣∣7(1−k)+5(k+2)+3(−2−1)2∣∣∣=0
=>7−7k+5k+10−9=0
=>2k=8
=>k=4
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