Consider the following two lines:

Line 1: Passes through \((-7, 0)\) and \((-7, -10)\)

Line 2: Passes through \((-1, -2)\) and \((-1, -10)\)

The slope of Line 1 is \(m = \frac{10}{0}\).

The slope of Line 2 is \(m = \frac{-8}{0}\).

Which of the following is true?
A. Line 1 is parallel to Line 2.
B. Line 1 is perpendicular to Line 2.
C. Line 1 is neither parallel nor perpendicular to Line 2.



Answer :

Sure, let's solve the problem step-by-step.

### Step 1: Understand the given coordinates.
We have two lines with the following coordinates:
- Line 1: passes through points \((-7, 0)\) and \((-7, -10)\).
- Line 2: passes through points \((-1, -2)\) and \((-1, -10)\).

### Step 2: Calculate the slopes.
The slope of a line passing through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

For Line 1:
- Coordinates: \((-7, 0)\) and \((-7, -10)\).
[tex]\[ m_1 = \frac{-10 - 0}{-7 - (-7)} = \frac{-10}{0} \][/tex]

Since the denominator is 0, this slope calculation becomes undefined. This indicates that Line 1 is a vertical line.

For Line 2:
- Coordinates: \((-1, -2)\) and \((-1, -10)\).
[tex]\[ m_2 = \frac{-10 - (-2)}{-1 - (-1)} = \frac{-10 + 2}{-1 + 1} = \frac{-8}{0} \][/tex]

Similarly, since the denominator is 0, this slope calculation also becomes undefined. This indicates that Line 2 is also a vertical line.

### Step 3: Determine the relationship between the lines.
Both Line 1 and Line 2 are vertical lines, which means they have the same slope (undefined).

### Conclusion:
If both lines have the same slope and are vertical lines, they are parallel to each other.

So, the correct statement is:
- Line 1 is parallel to Line 2

The final answer is therefore:
```
Line 1 is parallel to Line 2
```