For each of the following points write the quadrant in which it lies.
(i) `(-6, 3)` (ii) `(-5, -3)` (iii) (11, 6) (iv) `(1, -4)`
(v) `(-7, -4)` (vi) `(4, -1)` (vii) `(-3, 8)` (viii) `(3, -8)`

Answer

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

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

Now, let's analyze each point step by step:

### Step 1: Analyze Point (-6, 3)
- x = -6 (negative), y = 3 (positive)
- This point lies in the **Second Quadrant (II)**.

### Step 2: Analyze Point (-5, -3)
- x = -5 (negative), y = -3 (negative)
- This point lies in the **Third Quadrant (III)**.

### Step 3: Analyze Point (11, 6)
- x = 11 (positive), y = 6 (positive)
- This point lies in the **First Quadrant (I)**.

### Step 4: Analyze Point (1, -4)
- x = 1 (positive), y = -4 (negative)
- This point lies in the **Fourth Quadrant (IV)**.

### Step 5: Analyze Point (-7, -4)
- x = -7 (negative), y = -4 (negative)
- This point lies in the **Third Quadrant (III)**.

### Step 6: Analyze Point (4, -1)
- x = 4 (positive), y = -1 (negative)
- This point lies in the **Fourth Quadrant (IV)**.

### Step 7: Analyze Point (-3, 8)
- x = -3 (negative), y = 8 (positive)
- This point lies in the **Second Quadrant (II)**.

### Step 8: Analyze Point (3, -8)
- x = 3 (positive), y = -8 (negative)
- This point lies in the **Fourth Quadrant (IV)**.

### Summary of Quadrants:
1. (-6, 3) - Second Quadrant (II)
2. (-5, -3) - Third Quadrant (III)
3. (11, 6) - First Quadrant (I)
4. (1, -4) - Fourth Quadrant (IV)
5. (-7, -4) - Third Quadrant (III)
6. (4, -1) - Fourth Quadrant (IV)
7. (-3, 8) - Second Quadrant (II)
8. (3, -8) - Fourth Quadrant (IV)