Question

In what ratio does the y-axis divide the join of P(–4, 2) and Q(8, 3)?

Options

• 3 : 1

• 1 : 3

• 2 : 1

• 1 : 2

Answer 1

1 : 2

Explanation:

Let the y-axis meet PQ at R and let PR : RQ = k : 1. 

By the section formula, the x-coordinate of R is `x = (k xx x_2 + x_1)/(k + 1)`. 

Setting x = 0 with x₁ = –4 and x₂ = 8 gives `0 = (8k - 4)/(k + 1)` 

⇒ 8k – 4 = 0

⇒ `k = 1/2` 

So, `PR : RQ = 1/2 : 1 = 1 : 2`.