A straight fence runs from \(P(-6,\,1)\) to \(Q(3,\,7)\) on a farm plan and crosses the y-axis at the point \(R\). What is \(PR:RQ\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2 : 1
Every point on the y-axis has x-coordinate 0. So the section formula for the x-coordinate, with the unknown ratio \(k:1\), is set equal to 0.
Let R divide PQ in the ratio \(k:1\), with \(P(-6,\,1)\) and \(Q(3,\,7)\)
x-coordinate of R \(\displaystyle =\frac{k(3)+1(-6)}{k+1}=\frac{3k-6}{k+1}\)
On the y-axis: \(3k-6=0\), so \(k=2\)
Ratio \(=2:1\)
Check: y-coordinate \(\displaystyle =\frac{2(7)+1(1)}{2+1}=\frac{15}{3}=5\), so \(R=(0,\,5)\)
