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Question

The point A divides the line segment joining the points (−5,1) and (3,5) in the ratio k:1. The coordinates of points B and C are (1,5) and (7,−2) respectively. If the area of △ABC is 2 square units, then the number of values of k is

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
Given points are (5,1) and (3,5) and the ratio is k:1,
So, the point A=(3k5k+1,5k+1k+1)

Point B=(1,5), C=(7,2)
Now, the area of ABC
2=12|x1(y2y3)+x2(y3y1)+x3(y1y2)|
2=123k5k+1(5+2)+1(25k+1k+1)+7(5k+1k+15)4=21k355k1+35k+7k+123551k29k+137=±414k66k+1=±414k66=±(4k+4)14k66=4k+4 or 14k66=4k4k=7,319

Hence, the number of values of k is 2.

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