Question

Points A, B, C and D divide the join of O(0, 0) and P(0, 10) into five equal parts. The co-ordinates of point D are ______.

Options

• (10, 8)

• (−8, 0)

• (−10, 0)

• (0, 8)

Answer 1

Points A, B, C and D divide the join of O(0, 0) and P(0, 10) into five equal parts. The co-ordinates of point D are (0, 8).

Explanation:

From figure,

D divides the line segment OP in the ratio 4 : 1.

Let co-ordinates of D be (x, y).

By section-formula,

(x, y) = `((m_1x_2 + m_2x_1)/(m_1 + m_2), (m_1y_2 + m_2y_1)/(m_1 + m_2))`

Substituting values we get:

⇒ (x, y) = `((4×0+1×0)/(4+1)​, (4×10+1×0)/(4+1)​)`

= `(0/5, 40/5)`

= (0, 8)