In what ratio does the x-axis divide the line segment joining the points (3, -4) and (2, 6)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2 : 3
Every point on the x-axis has y-coordinate 0. Let the x-axis divide the segment joining A(3, −4) and B(2, 6) in the ratio \(k:1\); by the section formula, the y-coordinate of the point of division is then set equal to 0.
y-coordinate of the point of division: \(\displaystyle y=\frac{k\times6+1\times(-4)}{k+1}=0\)
\(6k-4=0\)
\(\displaystyle k=\frac{2}{3}\)
Ratio in which the x-axis divides AB \(\displaystyle =\frac{2}{3}:1=2:3\)
Shortcut: A has a negative and B a positive y-coordinate, so the axis cuts the segment between them, and the ratio is the ratio of their distances from the x-axis.
A is 4 units and B is 6 units from the x-axis
Ratio of the distances \(=4:6=2:3\)