First slide

Cartesian plane

Question

if the points $A (λ, 2 λ), B (3 λ, 3 λ)$ and $C (3, 1)$ are collinear, then $λ =$

Moderate

A

1/3
B

-1/3
C

2/3
D

-2/3

Solution

If points $A (λ, 2 λ), B (3 λ, 3 λ)$ and $C (3, 1)$ are collinear, then
$\begin{array}{l} |\begin{array}{ccc} λ & 2 λ & 1 \\ 3 λ & 3 λ & 1 \\ 3 & 1 & 1 \end{array}| = 0 \\ \Rightarrow λ (3 λ - 1) - 2 λ (3 λ - 3) + (3 λ - 9 λ) = 0 \\ \Rightarrow λ (3 λ + 1) = 0 \Rightarrow λ = - \frac{1}{3} [∵ λ \neq 0] \end{array}$

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