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Mathematics — CBSE Class 10 board question

Q1. [1]
The line represented by $\dfrac{x}{4} + \dfrac{y}{6} = 1$ intersects x-axis and y-axis respectively at P and Q. The coordinates of the mid-point of line segment PQ are:
  1. A $(2, 3)$
  2. B $(3, 2)$
  3. C $(2, 0)$
  4. D $(0, 3)$
Previously asked in CBSE board exam
2025 30/3/1 Q6
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer

The line $\dfrac{x}{4} + \dfrac{y}{6} = 1$ meets the x-axis at P(4, 0) and y-axis at Q(0, 6). Mid-point $= \left(\dfrac{4+0}{2}, \dfrac{0+6}{2}\right) = **(2, 3)$. Answer: A

Explanation

Set y = 0 to find P (x-intercept) and x = 0 to find Q (y-intercept), then apply the midpoint formula $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$. This is a direct application of the midpoint formula from Chapter 7.

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