In what ratio does the x-axis divide the line segment joining \(A(2,\,-6)\) and \(B(7,\,3)\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2 : 1
Let the x-axis cut AB at R in the ratio \(k:1\). R is on the x-axis, so the y-coordinate of R is 0.
y-coordinate of R by the section formula: \(\displaystyle \frac{k\times3+1\times(-6)}{k+1}\)
\(\displaystyle \frac{3k-6}{k+1}=0\), so \(3k-6=0\)
\(k=2\), so the ratio is \(2:1\)
Check: A is 6 units below the x-axis and B is 3 units above it, and \(6:3=2:1\)
