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Question
The points (1,1/2) and (3,-1/2) are
🎥 Video solution / Text Solution of this question is given below:
Given:
Points: \( A = (1, \frac{1}{2}) \), \( B = (3, -\frac{1}{2}) \)
Line: \( 2x + 3y = k \)
Step 1: Evaluate \( 2x + 3y \)
For A: \( 2(1) + 3\left(\frac{1}{2}\right) = \frac{7}{2} \)
For B: \( 2(3) + 3\left(-\frac{1}{2}\right) = \frac{9}{2} \)
✅ Option-wise Check:
- In between the lines \( 2x + 3y = -6 \) and \( 2x + 3y = 6 \): ✔️ True since \( \frac{7}{2}, \frac{9}{2} \in (-6, 6) \)
- On the same side of \( 2x + 3y = 6 \): ✔️ True, both values are less than 6
- On the same side of \( 2x + 3y = -6 \): ✔️ True, both values are greater than -6
- On the opposite side of \( 2x + 3y = -6 \): ❌ False, both are on the same side
✅ Final Answer:
The correct statements are:
- In between the lines \( 2x + 3y = -6 \) and \( 2x + 3y = 6 \)
- On the same side of the line \( 2x + 3y = 6 \)
- On the same side of the line \( 2x + 3y = -6 \)
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