Question

The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are:

Options

• A. (2, 4)

• B. (3, 5)

• C. (4, 2)

• D. (5, 3)

Answer 1

Let P(x, y) divides line segment joining A (1, 3) and B (4, 6) in the ratio 2 : 1.

We know that, the coordinates of a point (x, y) dividing the line segment joining the points (x₁, y₁) and (x₂, y₂) in the ratio m₁ : m₂ are given by

`x=(m_1x_2+m_2x_1)/(m_1+m_2)` and `y=(m_1+y_2+m_2y_1)/(m_1+m_2)`

`therefore Here x=(2(4)+1(1))/(2+1)` and `y=(2(6)+1(3))/(2+1)`

`rArrx=9/3 ` and `y=15/3`

`rArrx=3` and `y=3`

Thus, (3, 5) divides the line segment AB in the ratio 2 : 1.

Hence, the correct answer is B.