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In what ratio does the point (-4, 6) divide the line segment joining the points A(-6, 10) and B(3, -8) ?

Section Formula

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Answer

Let the point (-4, 6) divide the line segment joining the points A(-6, 10) and B(3, -8) in the ratio m : n

Using section-formula,

x-coordinate = (mx2+nx1m+n)\Big(\dfrac{mx2 + nx1}{m + n}\Big)

Comparing,

⇒−4=(m×3+n×(−6)m+n)⇒−4=3m−6nm+n⇒−4(m+n)=3m−6n⇒−4m−4n=3m−6n⇒−4m−3m=−6n+4n⇒−7m=−2n⇒mn=27⇒m:n=2:7.\Rightarrow -4 = \Big(\dfrac{m \times 3 + n \times (-6)}{m + n} \Big) \\[1em] \Rightarrow -4 = \dfrac{3m - 6n}{m + n} \\[1em] \Rightarrow -4(m + n) = 3m - 6n \\[1em] \Rightarrow -4m -4n = 3m - 6n \\[1em] \Rightarrow -4m - 3m = -6n + 4n \\[1em] \Rightarrow -7m = -2n \\[1em] \Rightarrow \dfrac{m}{n} = \dfrac{2}{7} \\[1em] \Rightarrow m : n = 2 : 7.

The ratio in which the point (-4, 6) divides the line segment is 2 : 7.

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