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Question

Choose the possible value of a such that point (3a, a) will be collinear with points (6,2) and (-4,-1).

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 2
To check whether the given points are collinear or not, we check the slopes.
The slope of any two points taken at a time out of the three points will always be the same.

Slope = y2y1x2x1

Finding slope from the given points :
Let, x1=4,x2=6y1=1, y2=2slope=(2+16+4)
= 310 (i)
Now taking x1=6,x2=3a y1=2, y2=a
slope = (a23a6)
= a23a6 (ii)
From the concept of collinearity
(i) = (ii)
310 = a23a6

3×(3a6)=10×(a2)
(9a18)=(10a20)
a=2
​​​​​​​a=2

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