Question

Show you’re thinking about your initial question of how to find the distance between the given points

Answer 1

To find the distance between two points in a Cartesian coordinate system, you can use the distance formula. Let’s say you have two points: \( P(x_1, y_1) \) and \( Q(x_2, y_2) \).

The distance \( d \) between these two points is given by the formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

### Steps to Calculate Distance:

1. **Identify the Coordinates**: Determine the coordinates of the two points you're interested in.
- For example, if \( P(3, 4) \) and \( Q(7, 1) \), then \( x_1 = 3, y_1 = 4, x_2 = 7, y_2 = 1 \).

2. **Substitute the Values into the Formula**:
\[
d = \sqrt{(7 - 3)^2 + (1 - 4)^2}
\]

3. **Calculate the Differences**:
- \( x_2 - x_1 = 7 - 3 = 4 \)
- \( y_2 - y_1 = 1 - 4 = -3 \)

4. **Square the Differences**:
- \( (4)^2 = 16 \)
- \( (-3)^2 = 9 \)

5. **Sum the Squares**:
\[
d = \sqrt{16 + 9} = \sqrt{25}
\]

6. **Find the Square Root**:
\[
d = 5
\]

### Conclusion:
The distance between the points \( P(3, 4) \) and \( Q(7, 1) \) is 5 units.

If you have specific points in mind, feel free to share them, and I can demonstrate the calculation using those coordinates!