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For what value of x, will the points (-1,x),(-3,2) and (-4,4)

Question

For what value of x, will the points (-1,x),(-3,2) and (-4,4) lie on a line?

A

-3

B

3

C

-2

D

2

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For what value of x, will the points (-1,x),(-3,2) and (-4,4) lie on a line?

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Text solutionVerified

A (- 1, x), B (- 3, 2), C (- 4, 4)

lie on a line

∴ \frac{1}{2} ∣ x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) ∣ = 0

\frac{1}{2} ∣ - 1 (2 - 4) + - 3 (4 - x) + - 4 (x - 2) ∣ = 0

\frac{1}{2} ∣ - 1 (- 2) - 3 (4 - x) - 4 (x - 2) ∣ = 0

\frac{1}{2} ∣ 2 - 3 \times 4 + 3 x - 4 x + 4 \times 2 ∣ = 0

\frac{1}{2} ∣ 2 - 12 + 3 x - 4 x + 8 ∣ = 0

\frac{1}{2} ∣ - 2 - x ∣ = 0

- 2 - x = 0

x = - 2

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Question Text	For what value of x, will the points (-1,x),(-3,2) and (-4,4) lie on a line?
Answer Type	Text solution:1
Upvotes	150