Question

Which of the following points lies on the graph of x = 2 ?

• A. (2, 0)
• B. (2, 1)
• C. (2, 2)
• D. all of these

Hint:

Remember that \(x = k\) is the equation of a vertical line passing through the x-axis at \(k\), and \(y = k\) is the equation of a horizontal line passing through the y-axis at \(k\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The equation \(x = 2\) represents a vertical line on the Cartesian plane. Every point on this line has an x-coordinate of exactly 2, while the y-coordinate can be any real number.

Step 2: Detailed Explanation:
We need to check which of the given points satisfy the condition that its x-coordinate is 2.
(A) (2, 0): The x-coordinate is 2. This point lies on the line.
(B) (2, 1): The x-coordinate is 2. This point lies on the line.
(C) (2, 2): The x-coordinate is 2. This point lies on the line.
Since all the points (A), (B), and (C) have an x-coordinate of 2, they all lie on the graph of \(x = 2\).

Step 3: Final Answer:
The correct option is all of these.