Question

Point M lies on the line segment joining the points A(6, 0) and B(0, 8) such that AM : BM = 2 : 3, the coordinates of point M are ______.

Options

• `(-16/5, 18/5)`

• `(18/5, -16/5)`

• `(16/5, 18/5)`

• `(18/5, 16/5)`

Answer 1

Point M lies on the line segment joining the points A(6, 0) and B(0, 8) such that AM : BM = 2 : 3, the coordinates of point M are `bbunderline((18/5, 16/5)`.

Explanation:

Apply the section formula:

The point dividing A(x₁, y₁) and B(x₂, y₂) internally in ratio m₁ : m₂ has coordinates,

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

With m₁ = 2, m₂ = 3, A(6, 0), B(0, 8),

This gives M = `(18/5, 16/5)`