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Mathematics

The coordinates of the point P which divides the join of A(5, -2) and B(9, 6) in the ratio 3 : 1 are :

  1. (4, -7)

  2. (72,4)\Big(\dfrac{7}{2}, 4\Big)

  3. (8, 4)

  4. (12, 8)

Section Formula

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Answer

Let point P be (x, y).

The coordinates of the point P which divides the join of A(5, -2) and B(9, 6) in the ratio 3 : 1 are : Reflection, RSA Mathematics Solutions ICSE Class 10.

Given,

m1 : m2 = 3 : 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 we get :

⇒(x,y)=(3×9+1×53+1,3×6+1×−23+1)=(27+54,18−24)=(324,164)=(8,4).\Rightarrow (x, y) = \Big(\dfrac{3 \times 9 + 1 \times 5}{3 + 1}, \dfrac{3 \times 6 + 1 \times -2}{3 + 1}\Big) \\[1em] = \Big(\dfrac{27 + 5}{4}, \dfrac{18 - 2}{4}\Big) \\[1em] = \Big(\dfrac{32}{4}, \dfrac{16}{4}\Big) \\[1em] = (8, 4).

Hence, Option 3 is the correct option.

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