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The ratio in which the point P(1, 2) divides the join of the points A(-2, 1) and B(7, 4) is:

  1. 1 : 2

  2. 2 : 1

  3. 3 : 2

  4. 2 : 3

Section Formula

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Answer

Let the ratio in which P divides AB be k : 1.

The ratio in which the point P(1, 2) divides the join of the points A(-2, 1) and B(7, 4) is: Reflection, RSA Mathematics Solutions ICSE Class 10.

By section-formula,

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

Using the y–coordinate to find ratio.

⇒2=(k(4)+1(1)k+1)⇒2=(4k+1k+1)⇒2(k+1)=4k+1⇒2k+2=4k+1⇒2−1=4k−2k⇒2k=1⇒k=12⇒k:1=12:1=1:2.\Rightarrow 2 = \Big(\dfrac{k(4) + 1(1)}{k + 1}\Big) \\[1em] \Rightarrow 2 = \Big(\dfrac{4k + 1}{k + 1}\Big) \\[1em] \Rightarrow 2(k + 1) = 4k + 1 \\[1em] \Rightarrow 2k + 2 = 4k + 1 \\[1em] \Rightarrow 2 - 1 = 4k - 2k \\[1em] \Rightarrow 2k = 1 \\[1em] \Rightarrow k = \dfrac{1}{2}\\[1em] \Rightarrow k : 1 = \dfrac{1}{2} : 1 = 1 : 2.

Hence, Option 1 is the correct option.

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