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
```
### 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
```
