1
Question
Value of p for which the points (-5, 1), (1, p) and (4, -2) are collinear is
Value of p for which the points (-5, 1), (1, p) and (4, -2) are collinear is
Open in App
Solution
The correct option is C -1
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)=(−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
=>−9p−9=0
=>p=−1
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)=(−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
=>−9p−9=0
=>p=−1
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
