First slide

Equation of line in Straight lines

Question

A light ray emerging from the point source placed at P(2,3) is reflected at a point Q on the y-axis. It then passes through the point R(5, 10). The coordinates of Q are

Moderate

A

(0, 3)
B

(0,2)
C

(0, 5)
D

none of these

Solution

The point of coincidence on they-axis is $Q (0, λ)$ .
The image of P(2,3) on the y-axis is P₁(-2,3). P₁, Q, and R are collinear. Therefore,
Slope of P₁ Q = Slope of P₁R

$\begin{array}{ll} or \frac{λ - 3}{0 - (- 2)} = \frac{10 - 3}{5 - (- 2)} \\ or λ - 3 = 2 \\ or λ = 5 \end{array}$
Therefore, the point Q is (0, 5).

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