Question

What is value of k if the points (2,-3),(k,-1) and(0,4) is collinear

Answer 1

Step-by-step explanation:

ANSWER

Given that the points A(2,3),B(4,k) and C(6,−3) are collinear.

As we know that if three points are collinear then they will lie of a same plane and thus will not form a triangle.

Therefore,

Area of triangle formed by these points will be 0

Therefore,

Now,

Area of △ formed by these points =

2

1

×

∣

∣

∣

∣

∣

∣

∣

∣

2

4

6

3

k

−3

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

Therefore,

∣

∣

∣

∣

∣

∣

∣

∣

2

4

6

3

k

−3

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

=0

[2(k−(−3))−3(4−6)+1((−12)−6k)]=0

2k+6+6−12−6k=0

−4k=0

⇒k=0

Thus the value of k is 0.

Hence the correct answer is 0.

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