In what ratio the line segment joining the points (-2, 3) and (3, -7) is divided by x-axis?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3 : 7
Every point on the x-axis has y-coordinate 0. A point that divides the segment in the ratio \(k:1\) has, by the section formula, y-coordinate \(\displaystyle\frac{k\,y_2+y_1}{k+1}\).
With \(A(-2,3)\) and \(B(3,-7)\): \(\displaystyle\frac{k(-7)+3}{k+1}=0\)
\(-7k+3=0\), so \(k=\displaystyle\frac{3}{7}\)
The ratio is \(3:7\), and the point is \(P\left(-\frac{1}{2},0\right)\)
Tip: The x-axis divides the segment in the ratio of the distances of the two points from it: A is 3 units above and B is 7 units below, so the ratio is 3 : 7 at once.