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Find a relation between x and y if the points (x, y), (1, 2) a

Question

Find a relation between $x$ and $y$ if the points $(x, y), (1, 2)$ and $(7, 0)$ are collinear.

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Camila Discussed

Find a relation between

x

and

y

if the points

(x, y), (1, 2)

and

(7, 0)

are collinear.

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

The given points are collinear then the area of triangle formed by these points will be 0

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

Here

(x_{1}, y_{1}) = (x, y)

(x_{2}, y_{2}) = (1, 2)

(x_{3}, y_{3}) = (7, 0)

⟹ \frac{1}{2} [x (2 - 0) + 1 (0 - y) + 7 (y - 2)] = 0

⟹ \frac{1}{2} [2 x - y + 7 y - 14] = 0

⟹ \frac{1}{2} [2 x + 6 y - 14] = 0

⟹ 2 x + 6 y - 14 = 0

⟹ x + 3 y - 7 = 0

Hence this is the required relation between

x

and

y

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Question Text	Find a relation between $x$ and $y$ if the points $(x, y), (1, 2)$ and $(7, 0)$ are collinear.
Answer Type	Text solution:1
Upvotes	150