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Mathematics

Line segment joining points (4, 3) and (1, -2) is divided by the point (y, 0) in the ratio :

  1. 2 : 3

  2. 3 : 2

  3. 3 : 4

  4. 4 : 2

Section Formula

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Answer

Let (y, 0) divide the line segment joining the points (4, 3) and (1, -2) in the ratio k : 1.

By section-formula,

(x, y) = (m1x2+m2x1m1+m2,m1y2+m2y1m1+m2)\Big(\dfrac{m1x2 + m2x1}{m1 + m2}, \dfrac{m1y2 + m2y1}{m1 + m2}\Big)

Substituting values for y-coordinate :

0=k×2+1×3k+12k+3=02k=3k=32.\Rightarrow 0 = \dfrac{k \times -2 + 1 \times 3}{k + 1} \\[1em] \Rightarrow -2k + 3 = 0 \\[1em] \Rightarrow 2k = 3 \\[1em] \Rightarrow k = \dfrac{3}{2}.

Substituting value of k in k : 1, we get :

32:1\dfrac{3}{2} : 1

⇒ 3 : 2.

Hence, Option 2 is the correct option.

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