find the distance btween P(1,-3) and Q(3,-4)

To find the distance between points \( P(1, -3) \) and \( Q(3, -4) \), we use the distance formula:

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

Given:
- \( P(x_1, y_1) = (1, -3) \)
- \( Q(x_2, y_2) = (3, -4) \)

Substitute the values:

\[
d = \sqrt{(3 - 1)^2 + (-4 + 3)^2}
\]

\[
= \sqrt{(2)^2 + (-1)^2}
\]

\[
= \sqrt{4 + 1}
\]

\[
= \sqrt{5}
\]

So, the distance between points \( P \) and \( Q \) is \( \sqrt{5} \).

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**Related Questions:**
1. How do you find the midpoint between two points?
2. What is the distance between the points \( (2, 3) \) and \( (-1, -2) \)?
3. How can you find the distance between points on a 3D plane?
4. Can the distance formula be derived from the Pythagorean Theorem?
5. What is the significance of the distance formula in coordinate geometry?

**Tip:** For easier calculations, keep square roots in radical form unless you need a decimal approximation.

Calculate the distance between points P(1, -3) and Q(3, -4) with a step-by-step guide. This problem uses the distance formula and explores coordinate geometry, suitable for students in Grades 7-9.

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