Question

A point on the x-axis divides the line segment joining the points A(2, −3) and B(5, 6) in the ratio 1 : 2. The point is __________.

Options

• (4, 0)

• `(7/2, 3/2)`

• (3, 0)

• (0, 3)

Answer 1

A point on the x-axis divides the line segment joining the points A(2, −3) and B(5, 6) in the ratio 1 : 2. The point is (3, 0).

Explanation:

Here, A(x₁, y₁) = (2, −3) and B(x₂, y₂) = (5, 6) and the ratio m : n = 1 : 2

X-coordinate:

x = `(mx_2 + nx_1)/(m + n)`

= `(1 xx 5 + 2 xx 2)/(1 + 2)`

= `(5 + 4)/3`

= `9/3`

= 3

Y-coordinate:

x = `(my_2 + ny_1)/(m + n)`

= `(1 xx 6 + 2 xx (-3))/(1 + 2)`

= `(6 - 6)/3`

= `0/3`

= 0