Problem Statement
Find the ratio in which the $y$-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$. Also find the point of intersection.
Verified Solution & Marking Scheme
Set Up Ratio k : 1
Point on $y$-axis has coordinates $(0, y)$. By section formula: $x = \frac{k(-1) + 1(5)}{k + 1} = 0 \implies -k + 5 = 0 \implies k = 5$.
State Ratio
The ratio is $5 : 1$.
Find y-Coordinate
$y = \frac{5(-4) + 1(-6)}{5 + 1} = \frac{-20 - 6}{6} = -\frac{26}{6} = -\frac{13}{3}$