In what ratio does the point (-4, 6) divide the line segment joining the points (-6, 10) and (3, -8)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2 : 7
By the section formula, the point dividing the join of \((x_1,y_1)\) and \((x_2,y_2)\) in the ratio \(m:n\) has \(\displaystyle x=\frac{mx_2+nx_1}{m+n}\). One coordinate is enough to find the ratio.
The point is \((-4,6)\), the ends are \((-6,10)\) as \((x_1,y_1)\) and \((3,-8)\) as \((x_2,y_2)\); using the x-coordinates: \(\displaystyle -4=\frac{3m+(-6)n}{m+n}\)
\(-4m-4n=3m-6n\), so \(2n=7m\) and the point divides the segment in the ratio \(m:n=2:7\)