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Condition of Concurrency of 3 Straight Lines

If the points...

Question

If the points $(0, 0), (1, 2)$ and $(x, y)$ are collinear, then

A

x = y

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B

2 x = y

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C

x = 2 y

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D

2 x = - y

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Solution

The correct option is D $2 x = y$
Forming the equation using first two points, $(0, 0)$ and $(1, 2)$ $y = \frac{2}{1} x$
Also $(x, y)$ satisfy this
$∴ y = 2 x$

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Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} x - y - z & 2 x & 2 x 2 y & y - z - x & 2 y 2 z & 2 z & z - x - y \end{matrix} ∣ ∣ ∣ ∣

Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} x + y + 2 z & x & y z & y + z + 2 x & y z & x & z + x + 2 y \end{matrix} ∣ ∣ ∣ ∣

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Condition of Concurrency of 3 Straight Lines

Standard XII Mathematics

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