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Find the relation between x and y if the points A(x, y), B(-5,

Question

Find the relation between $x$ and $y$ if the points $A (x, y), B (- 5, 7)$ and $C (- 4, 5)$ are collinear.

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Find the relation between

x

and

y

if the points

A (x, y), B (- 5, 7)

and

C (- 4, 5)

are collinear.

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

Area of triangle

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

= \frac{1}{2} [x (7 - 5) + 5 (5 - y) - 4 (4 - 7)]

Given

A, B

and

C

are collinear, then area of triangle must be zero.

∴ \frac{1}{2} [x (7 - 5) + 5 (5 - y) - 4 (4 - 7)] = 0

\Rightarrow \frac{1}{2} [2 x - 25 + 5 y - 4 y + 25] = 0

\Rightarrow \frac{1}{2} (2 x + y + 3) = 0

Then, relation between

x

and

y

2 x + y + 3 = 0

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Question Text	Find the relation between $x$ and $y$ if the points $A (x, y), B (- 5, 7)$ and $C (- 4, 5)$ are collinear.
Answer Type	Text solution:1
Upvotes	150