Fill in the blanks.
(P) Any point lying on x-axis is of the form ________.
(Q) The abscissa of a point on y-axis is _________.
(R) The point at which the two coordinate axes meet is called the ________.
(S) The perpendicular distance of the point (4, 5) from x-axis is ________.
(T) The perpendicular distance of the point (3, 7) from y-axis is ________.

Options

A. `{:(,(P), (Q), (R), (S), (T),),(,(0, y),1,"origin",5,3,):}`
B. `{:(,(P), (Q), (R), (S), (T),),(,(x, 0),0,"origin",5,3,):}`
C. `{:(,(P), (Q), (R), (S), (T),),(,(x, 0),0,"origin",3,5,):}`
D. `{:(,(P), (Q), (R), (S), (T),),(,(0, y),1,"origin",3,5,):}`

Answer

Let's solve the question step by step:

### Step 1: Understanding the x-axis
Any point lying on the x-axis has a y-coordinate of 0. Therefore, the coordinates of any point on the x-axis can be expressed as (x, 0), where x can be any real number.

**Hint:** Remember that the y-coordinate is always zero for points on the x-axis.

### Step 2: Understanding the y-axis
Any point lying on the y-axis has an x-coordinate of 0. Thus, the coordinates of any point on the y-axis can be expressed as (0, y), where y can be any real number.

**Hint:** The x-coordinate is always zero for points on the y-axis.

### Step 3: Intersection of the axes
The point at which the two coordinate axes (x-axis and y-axis) meet is called the origin. The coordinates of the origin are (0, 0).

**Hint:** Think about where the x-axis and y-axis intersect.

### Step 4: Perpendicular distance from the x-axis
The perpendicular distance of a point from the x-axis is simply the absolute value of its y-coordinate. For the point (4, 5), the y-coordinate is 5, so the distance is |5| = 5.

**Hint:** The distance from the x-axis is determined by the y-coordinate of the point.

### Step 5: Perpendicular distance from the y-axis
The perpendicular distance of a point from the y-axis is the absolute value of its x-coordinate. For the point (3, 7), the x-coordinate is 3, so the distance is |3| = 3.

**Hint:** The distance from the y-axis is determined by the x-coordinate of the point.

### Final Answers:
(P) Any point lying on the x-axis is of the form **(x, 0)**.
(Q) The abscissa of a point on the y-axis is **0**.
(R) The point at which the two coordinate axes meet is called the **origin**.
(S) The perpendicular distance of the point (4, 5) from the x-axis is **5**.
(T) The perpendicular distance of the point (3, 7) from the y-axis is **3**.