KnowledgeBoat Logo

Mathematics

The line segment joining the points M(5, 7) and N(-3, 2) is intersected by the y-axis at point L. Write down the abscissa of L. Hence, find the ratio in which L divides MN. Also, find the co-ordinates of L.

Section Formula

17 Likes

Answer

Since, L lies on y-axis let its co-ordinates be (0, y).

Let L divide MN in ratio m1 : m2.

By formula,

x=m1x2+m2x1m1+m20=m1×3+m2×5m1+m20=3m1+5m23m1=5m2m1m2=53.\Rightarrow x = \dfrac{m1x2 + m2x1}{m1 + m2} \\[1em] \Rightarrow 0 = \dfrac{m1 \times -3 + m2 \times 5}{m1 + m2} \\[1em] \Rightarrow 0 = -3m1 + 5m2 \\[1em] \Rightarrow 3m1 = 5m2 \\[1em] \Rightarrow \dfrac{m1}{m2} = \dfrac{5}{3}.

m1 : m2 = 5 : 3.

By formula,

y=m1y2+m2y1m1+m2y=5×2+3×75+3y=10+218y=318.\Rightarrow y = \dfrac{m1y2 + m2y1}{m1 + m2} \\[1em] \Rightarrow y = \dfrac{5 \times 2 + 3 \times 7}{5 + 3} \\[1em] \Rightarrow y = \dfrac{10 + 21}{8} \\[1em] \Rightarrow y = \dfrac{31}{8}.

Hence, abscissa of L = 0, m1 : m2 = 5 : 3 and co-ordinates of L = (0,318)\Big(0, \dfrac{31}{8}\Big).

Answered By

11 Likes


Related Questions