Question

$QUESTION$


Find a relation between x and y of the points A(x,y),B(-4,6) and C(-2,3) are collinear



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Answer 1

Answer:

If three points (x₁, y₁), (x₂, y₂) and (x₃, y₃) are collinear,

then [x₁(y₂ - y₃) + x₂( y₃ - y₁)+ x₃(y₁ - y₂)] = 0

Take, (x₁, y₁) = (x, y)

(x₂, y₂) = ( - 4,6)

and (x₃, y₃) = ( - 2 ,3)

Then, Using property of collinear points:

[x(6 - 3) + (-4)( 3 - y) + (-2)(y - 6)] = 0

⇒ 3x - 12 + 4y - 2y + 12 = 0

⇒ 3x + 2y = 0

⇒ y=\frac{-3x}{2}y=

2

−3x

Step-by-step explanation:

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Answer 2

Answer:

If three points (x₁, y₁), (x₂, y₂) and (x₃, y₃) are collinear,

then [x₁(y₂ - y₃) + x₂( y₃ - y₁)+ x₃(y₁ - y₂)] = 0

Take, (x₁, y₁) = (x, y)

(x₂, y₂) = ( - 4,6)

and (x₃, y₃) = ( - 2 ,3)

Then, Using property of collinear points:

[x(6 - 3) + (-4)( 3 - y) + (-2)(y - 6)] = 0

⇒ 3x - 12 + 4y - 2y + 12 = 0

⇒ 3x + 2y = 0

$y = \frac{ - 3x}{2}$