The distance between the points (0,0) and the intersecting point of the graphs of x= 3 and y = 4 is

Options

A. 4 unit
B. 3 unit
C. 2 unit
D. 5 unit

Answer

To find the distance between the points (0,0) and the intersecting point of the graphs of x = 3 and y = 4, we can follow these steps:

### Step 1: Identify the Points
The first point is (0, 0), which is the origin. The second point is where the lines x = 3 and y = 4 intersect. This point is (3, 4).

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

### Step 3: Substitute the Coordinates
Here, we have:
- \( (x_1, y_1) = (0, 0) \)
- \( (x_2, y_2) = (3, 4) \)

Substituting these values into the distance formula:
\[ d = \sqrt{(3 - 0)^2 + (4 - 0)^2} \]

### Step 4: Calculate the Differences
Now calculate the differences:
\[ d = \sqrt{(3)^2 + (4)^2} \]

### Step 5: Square the Differences
Calculate the squares:
\[ d = \sqrt{9 + 16} \]

### Step 6: Add the Squares
Now add the results:
\[ d = \sqrt{25} \]

### Step 7: Take the Square Root
Finally, take the square root:
\[ d = 5 \]

### Conclusion
The distance between the points (0, 0) and (3, 4) is 5.

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