Read the following statements carefully and state T' for True and 'F' for False.
P. Two points having same abscissae but different ordinates, lies on a line parallel to y-axis.
Q. The abscissa of a point on y-axis is always equal to its ordinate.
R. The point at which the two coordinate axes meet is called the origin
S. The signs of abscissae and ordinates are same in the quadrant I and IV.
T. The perpendicular distance of the point (2,8) from y-axis is 8 units.

Options

A. `{:(P, Q, R, S, T),(T, T, T, F, T):}`
B. `{:(P, Q, R, S, T),(F, T, F, T, F):}`
C. `{:(P, Q, R, S, T),(T, F, T, F, F):}`
D. `{:(P, Q, R, S, T),(T, F, T, F, T):}`

Answer

To solve the problem, we will evaluate each statement one by one and determine whether they are true (T) or false (F).

### Step-by-Step Solution:

1. **Statement P**: "Two points having same abscissae but different ordinates, lies on a line parallel to y-axis."
- **Explanation**: If two points have the same abscissa (x-coordinate) but different ordinates (y-coordinates), they will lie vertically above or below each other on the Cartesian plane. This means they will form a vertical line, which is parallel to the y-axis.
- **Conclusion**: This statement is **True (T)**.

2. **Statement Q**: "The abscissa of a point on y-axis is always equal to its ordinate."
- **Explanation**: The abscissa (x-coordinate) of any point on the y-axis is always 0, while the ordinate (y-coordinate) can be any value (positive, negative, or zero). Therefore, the abscissa is not equal to the ordinate unless the point is the origin (0,0).
- **Conclusion**: This statement is **False (F)**.

3. **Statement R**: "The point at which the two coordinate axes meet is called the origin."
- **Explanation**: The origin is defined as the point where the x-axis and y-axis intersect, which is at the coordinates (0,0).
- **Conclusion**: This statement is **True (T)**.

4. **Statement S**: "The signs of abscissae and ordinates are same in the quadrant I and IV."
- **Explanation**: In Quadrant I, both x (abscissa) and y (ordinate) are positive. In Quadrant IV, the x (abscissa) is positive and y (ordinate) is negative. Therefore, the signs are not the same in these quadrants.
- **Conclusion**: This statement is **False (F)**.

5. **Statement T**: "The perpendicular distance of the point (2,8) from y-axis is 8 units."
- **Explanation**: The perpendicular distance from the y-axis to a point (x,y) is given by the absolute value of the x-coordinate. For the point (2,8), the distance from the y-axis is |2| = 2 units, not 8 units.
- **Conclusion**: This statement is **False (F)**.

### Final Answers:
- P: T
- Q: F
- R: T
- S: F
- T: F

### Summary of Results:
- P: T
- Q: F
- R: T
- S: F
- T: F