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For what value of x are the points A(-3, 12), B(7, 6) and C(x,

Question

For what value of x are the points $A (- 3, 12)$ , $B (7, 6)$ and $C (x, 9)$ collinear?

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Elijah Discussed

For what value of x are the points

A (- 3, 12)

B (7, 6)

and

C (x, 9)

collinear?

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Points are

A (- 3, 12), B (7, 6)

and

C (x, 9)

are collinear.

Which means area of triangle ABC

= 0

Area of a triangle

= \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]

= \frac{1}{2} [- 3 (6 - 9) + 7 (9 - 12) + x (12 - 6)]

= \frac{1}{2} [- 3 \times (- 3) + 7 \times (- 3) + x \times 6]

= \frac{1}{2} [9 - 21 + 6 x]

= \frac{1}{2} [6 x - 12]

Since points are collinear:

\frac{1}{2} (6 x - 12) = 0

x = 2

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Question Text	For what value of x are the points $A (- 3, 12)$ , $B (7, 6)$ and $C (x, 9)$ collinear?
Answer Type	Text solution:1
Upvotes	150