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Question

If the points X(a, b + c), Y(b, a + c) and Z(k, a + b) are collinear, then the value of k is

A
(a + b + c)
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B
-c
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C
b
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D
c
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Solution

The correct option is D c
If the three points X, Y and Z are collinear, then, the area of triangle XYZ is zero.

12|a(a+cab)+b(a+bbc)+k(b+cac)|=0

12|a(cb)+b(ac)+k(ba)|=0

12|acab+babc+kbka|=0

acbc+kbka=0

k(ba)=c(ba)

k=c

Hence, the correct answer is option (d).

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