Find the ratio in which the y-axis divides the line segment joining the points (-8, 1) and (4, 5).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2:1
Every point on the y-axis has x-coordinate 0. By the section formula, the point dividing the join of \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(k:1\) has x-coordinate \(\displaystyle \frac{kx_2+x_1}{k+1}\), so this x-coordinate is set equal to 0.
With \(x_1=-8\) and \(x_2=4\): \(\displaystyle \frac{4k+(-8)}{k+1}=0\)
The numerator must be zero: \(4k-8=0\), so \(k=2\)
The ratio is \(2:1\)
Shortcut: The y-axis divides the join in the ratio of the distances of the two points from it: \(|-8|:|4|=8:4=2:1\).