Question

If point \(R(a,b)\) lies on the line segment joining \(P(0,0)\) and \(Q(0,2)\), which of the following is true?

• A. \(a=0\)
• B. \(a=2\)
• C. \(b=0\)
• D. None of these

Hint:

If two end points share the same \(x\) (or \(y\)) coordinate, the whole segment is a vertical (or horizontal) line with that coordinate fixed.

Answer 1

The Correct Option is A

Step 1: Observe the segment \(PQ\).
Both \(P\) and \(Q\) have \(x\)-coordinate \(0\), so the segment \(PQ\) lies on the vertical line \(x=0\).
Step 2: Conclude for any point on the segment.
Any point \(R(a,b)\) on this segment must satisfy \(a=0\) and \(0\le b\le 2\).