KnowledgeBoat Logo

Mathematics

Calculate the ratio in which the line joining the points (-3, -1) and (5, 7) is divided by the line x = 2. Also, find the co-ordinates of the point of intersection.

Section Formula

15 Likes

Answer

Let point of intersection be (2, y). [∵ any point on the line x = 2 has x co-ordinate = 2]

By formula,

x=m1x2+m2x1m1+m22=m1×5+m2×3m1+m22m1+2m2=5m13m25m12m1=2m2+3m23m1=5m2m1m2=53.x = \dfrac{m1x2 + m2x1}{m1 + m2} \\[1em] \Rightarrow 2 = \dfrac{m1 \times 5 + m2 \times -3}{m1 + m2} \\[1em] \Rightarrow 2m1 + 2m2 = 5m1 - 3m2 \\[1em] \Rightarrow 5m1 - 2m1 = 2m2 + 3m2 \\[1em] \Rightarrow 3m1 = 5m2 \\[1em] \Rightarrow \dfrac{m1}{m2} = \dfrac{5}{3}.

m1 : m2 = 5 : 3.

y=m1y2+m2y1m1+m2=5×7+3×15+3=3538=328=4.y = \dfrac{m1y2 + m2y1}{m1 + m2} \\[1em] = \dfrac{5 \times 7 + 3 \times -1}{5 + 3} \\[1em] = \dfrac{35 - 3}{8} \\[1em] = \dfrac{32}{8} \\[1em] = 4.

Hence, co-ordinates of point of intersection = (2, 4) and ratio = 5 : 3.

Answered By

10 Likes


Related Questions