The distance between the line `2x+4 =0 and x-5=0` is

Options

A. 9 units
B. 1 units
C. 5 units
D. 7 units

Answer

To find the distance between the lines given by the equations \(2x + 4 = 0\) and \(x - 5 = 0\), we will follow these steps:

### Step 1: Identify the equations of the lines
The equations given are:
1. \(2x + 4 = 0\)
2. \(x - 5 = 0\)

### Step 2: Solve for x in each equation
For the first equation:
\[ 2x + 4 = 0 \implies 2x = -4 \implies x = -2 \]

For the second equation:
\[ x - 5 = 0 \implies x = 5 \]

### Step 3: Determine the coordinates of the points on the lines
Since both equations do not involve the variable \(y\), we can assume \(y = 0\) for both lines. Therefore, the coordinates of the points on the lines are:
- For the first line: \((-2, 0)\)
- For the second line: \((5, 0)\)

### Step 4: Use the distance formula to find the distance between the two points
The distance \(D\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:
\[ D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the coordinates we found:
\[ D = \sqrt{(5 - (-2))^2 + (0 - 0)^2} \]
\[ D = \sqrt{(5 + 2)^2 + 0^2} \]
\[ D = \sqrt{(7)^2} \]
\[ D = \sqrt{49} = 7 \]

### Conclusion
The distance between the lines \(2x + 4 = 0\) and \(x - 5 = 0\) is \(7\) units.

---