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(1,6), (3.-2) and (-2,K) are collinear points. What is K?

Question

$(1, 6), (3. - 2)$ and $(- 2, K)$ are collinear points. What is $K$ ?

- 6

2

8

10

18

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Elizabeth Discussed

(1, 6), (3. - 2)

and

(- 2, K)

are collinear points. What is

K

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

If three points are collinear then the area of triangle is zero.

Therefore, if the points

(1, 6)

(3, - 2)

and

(- 2, K)

are collinear, then their area must be zero that is:

A = \frac{1}{2} ∣ x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) ∣ \Rightarrow 0 = \frac{1}{2} ∣ 1 (- 2 - K) + 3 (K - 6) - 2 (6 + 2) ∣ \Rightarrow 0 = ∣ - 2 - K + 3 K - 18 - 16 ∣ \Rightarrow 0 = ∣ 2 K - 36 ∣ \Rightarrow 2 K - 36 = 0 \Rightarrow 2 K = 36 \Rightarrow K = 18

Hence,

K = 18

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Question Text	$(1, 6), (3. - 2)$ and $(- 2, K)$ are collinear points. What is $K$ ?
Answer Type	Text solution:1
Upvotes	150