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 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.
Show Hint
To find the division points of a line segment, use the section formula for internal division.
Updated On: Dec 11, 2025
- \( (4, 0), (5, 2) \)
- \( (0, 4), (5, 2) \)
- \( (4, 0), (2, 5) \)
- \( (0, 4), (2, 5) \)
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The Correct Option is A
Solution and Explanation
We divide the line segment into three equal parts. The coordinates of the division points can be calculated using the section formula:
\[
{Point 1} = \left( \frac{2 \cdot 6 + 1 \cdot 3}{3}, \frac{2 \cdot 4 + 1 \cdot (-2)}{3} \right) = (4, 0)
\]
\[
{Point 2} = \left( \frac{1 \cdot 6 + 2 \cdot 3}{3}, \frac{1 \cdot 4 + 2 \cdot (-2)}{3} \right) = (5, 2)
\]
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