In which quadrant does the given points lie
(i) `(4,-2)`
(ii) `(-2,-2)`
(iii) `(4,3)`
(iv) `(-3,4)`

Explanation

To determine in which quadrant each of the given points lies, we need to analyze the signs of their x and y coordinates. The Cartesian plane is divided into four quadrants based on the signs of the coordinates:

1. **First Quadrant (I)**: x > 0 and y > 0
2. **Second Quadrant (II)**: x < 0 and y > 0
3. **Third Quadrant (III)**: x < 0 and y < 0
4. **Fourth Quadrant (IV)**: x > 0 and y < 0

Now, let's analyze each point:

### Step 1: Analyze the point `(4, -2)`
- x = 4 (positive)
- y = -2 (negative)
- Since x is positive and y is negative, this point lies in the **Fourth Quadrant (IV)**.

### Step 2: Analyze the point `(-2, -2)`
- x = -2 (negative)
- y = -2 (negative)
- Since both x and y are negative, this point lies in the **Third Quadrant (III)**.

### Step 3: Analyze the point `(4, 3)`
- x = 4 (positive)
- y = 3 (positive)
- Since both x and y are positive, this point lies in the **First Quadrant (I)**.

### Step 4: Analyze the point `(-3, 4)`
- x = -3 (negative)
- y = 4 (positive)
- Since x is negative and y is positive, this point lies in the **Second Quadrant (II)**.

### Summary of Quadrants:
- (4, -2) → Fourth Quadrant (IV)
- (-2, -2) → Third Quadrant (III)
- (4, 3) → First Quadrant (I)
- (-3, 4) → Second Quadrant (II)