Question

Two points having the same abscissae but different ordinates lie on:

• A. x-axis
• B. y-axis
• C. a line parallel to the y-axis
• D. a line parallel to the x-axis

Hint:

Points with the same abscissa (x-coordinate) but different ordinates (y-coordinates) lie on a vertical line parallel to the y-axis. This is because their x-coordinates remain constant, while their y-coordinates vary.

Answer 1

The Correct Option is C

Step 1: Understand the Problem.
The abscissa of a point refers to its x-coordinate, and the ordinate refers to its y-coordinate. If two points have the same abscissa but different ordinates, their x-coordinates are identical, while their y-coordinates differ. Step 2: Analyze Each Option.
Let the two points be $ P(x_1, y_1) $ and $ Q(x_1, y_2) $, where $ x_1 $ is the same for both points, but $ y_1 \neq y_2 $. 1. x-axis:
Points on the x-axis have $ y = 0 $. Since the ordinates are different, these points cannot lie on the x-axis. 2. y-axis:
Points on the y-axis have $ x = 0 $. Since the abscissae are the same but not necessarily zero, these points do not necessarily lie on the y-axis. 3. a line parallel to the y-axis:
A line parallel to the y-axis has a constant x-coordinate. Since both points have the same x-coordinate, they lie on a vertical line parallel to the y-axis. 4. a line parallel to the x-axis:
A line parallel to the x-axis has a constant y-coordinate. Since the ordinates are different, these points do not lie on a horizontal line. Step 3: Analyze the Options.
Option (1): x-axis — Incorrect, as the ordinates are different.
Option (2): y-axis — Incorrect, as the abscissae are not necessarily zero.
Option (3): a line parallel to the y-axis — Correct, as points with the same abscissa lie on a vertical line.
Option (4): a line parallel to the x-axis — Incorrect, as the ordinates are different.
Step 4: Final Answer. $$ (3) \mathbf{\text{a line parallel to the y-axis}} $$