Question

A line segment with the end points \( A(3,-2) \) and \( B(6,4) \) is divided into three equal parts. Find the coordinates of the division points.

• A. \( (4, 0), (5, 2) \)
• B. \( (0, 4), (5, 2) \)
• C. \( (4, 0), (2, 5) \)
• D. \( (0, 4), (2, 5) \)

Hint:

To find the division points of a line segment, use the section formula for internal division.

Answer 1

The Correct Option is A

We divide the line segment into three equal parts. The coordinates of the division points can be calculated using the section formula: \[ {Point 1} = \left( \frac{2 \cdot 6 + 1 \cdot 3}{3}, \frac{2 \cdot 4 + 1 \cdot (-2)}{3} \right) = (4, 0) \] \[ {Point 2} = \left( \frac{1 \cdot 6 + 2 \cdot 3}{3}, \frac{1 \cdot 4 + 2 \cdot (-2)}{3} \right) = (5, 2) \]