the value of 2*3*4*
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collinear means points in the same line
i.e. if these points are collinear, it means that these points lie on the same line.
now assume that these three points make a triangle..since these points lie on the same line, so the area covered by these three points is zero.
using area of a triangle formula,
area =1/2[x1(y2−y3)+x2(y3−y1)+x3(y1−y2))]=0
Therefore Condition for collinearity,
x
1
y
2
+x
2
y
3
+x
3
y
1
=x
2
y
1
+x
3
y
2
+x
1
y
3
Here,
x
1
=a,y
1
=a,x
2
=2,y
2
=3 and x
3
=4,y
3
=−1
Put this in above equation, we get
⇒3a−2+4a=2a+12−a
⇒7a−2=12+a⇒6a=14⇒a=14/6 or 7/3
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