In the given graph, P and Q are points such that PQ cuts off intercepts of 5 units and 3 units along the x-axis and y-axis respectively. Line RS is perpendicular to PQ and passes through the origin.
Find:
(a) the coordinates of P and Q.
(b) the equation of RS.
(a) From the graph:
P = (5, 0) and Q = (0, −3).
(b) Slope of PQ = \frac{-3-0}{0-5}=\frac{-3}{-5}=\frac{3}{5}
Since RS is perpendicular to PQ:
Slope of RS × \frac{3}{5} = −1
⇒ Slope of RS = -\frac{5}{3}
RS passes through the origin (0, 0).
Using y − y₁ = m(x − x₁):
y − 0 = -\frac{5}{3}(x − 0)
⇒ y = -\frac{5\mathrm{x}}{3}
⇒ 3y = −5x
⇒ 5x + 3y = 0
Therefore, the equation of RS is 5x + 3y = 0.
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