Question

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 the:

1. coordinates of P and Q 
2. equation of line RS

Answer 1

(a) From the graph

The coordinates of

P = (5, 0)

Q = (0,−3)

(b) Slope of PQ (m₁) = `(y_2 − y_1)/(x_2 − x_1)`

Slope of PQ (m₁) = `(y_2 − y_1)/(x_2 − x_1)`

Since line RS is perpendicular to PQ the slopе

m2 of RS is 

m_{1 −} m₂ = −1

m₂ = `−1/3 = (−5)/3`

m₂ = `3/5`

Now, equation of line RS passing through origin (0, 0)

(y − y1) = `(−5)/3 (x − x_1)`

`(y − 0) = (−5)/3 (x − 0)`

3y + 5x = 0