How the following pairs of points are placed w.r.t the line 3x-8y-7=0?
`(i) (-3,-4) and (1,2) " " (ii) (-1,-1) and (3,7)`

Explanation

To determine how the given pairs of points are placed with respect to the line \(3x - 8y - 7 = 0\), we will follow these steps:

### Step 1: Identify the line equation
The equation of the line is given as:
\[ 3x - 8y - 7 = 0 \]

### Step 2: Substitute the points into the line equation
For each point \((x, y)\), we will substitute the coordinates into the expression \(3x - 8y - 7\) to determine its position relative to the line.

### Step 3: Analyze the first pair of points \((-3, -4)\) and \((1, 2)\)

#### Point 1: \((-3, -4)\)
Substituting \((-3, -4)\) into the line equation:
\[ 3(-3) - 8(-4) - 7 = -9 + 32 - 7 = 16 \]
Since \(16 > 0\), the point \((-3, -4)\) is above the line.

#### Point 2: \((1, 2)\)
Substituting \((1, 2)\) into the line equation:
\[ 3(1) - 8(2) - 7 = 3 - 16 - 7 = -20 \]
Since \(-20 < 0\), the point \((1, 2)\) is below the line.

### Step 4: Determine the relationship between the points
Since one point is above the line and the other is below the line, we conclude that the points \((-3, -4)\) and \((1, 2)\) lie on different sides of the line.

### Step 5: Analyze the second pair of points \((-1, -1)\) and \((3, 7)\)

#### Point 1: \((-1, -1)\)
Substituting \((-1, -1)\) into the line equation:
\[ 3(-1) - 8(-1) - 7 = -3 + 8 - 7 = -2 \]
Since \(-2 < 0\), the point \((-1, -1)\) is below the line.

#### Point 2: \((3, 7)\)
Substituting \((3, 7)\) into the line equation:
\[ 3(3) - 8(7) - 7 = 9 - 56 - 7 = -54 \]
Since \(-54 < 0\), the point \((3, 7)\) is also below the line.

### Step 6: Determine the relationship between the points
Since both points are below the line, we conclude that the points \((-1, -1)\) and \((3, 7)\) lie on the same side of the line.

### Summary of Results
1. The points \((-3, -4)\) and \((1, 2)\) lie on different sides of the line.
2. The points \((-1, -1)\) and \((3, 7)\) lie on the same side of the line.