Find the distance between points *P*(3, 3) and *Q*(9, 7) to the nearest tenth.

To find the distance between the points \( P(3, 3) \) and \( Q(9, 7) \), we use the distance formula:

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

Here, \( (x_1, y_1) = (3, 3) \) and \( (x_2, y_2) = (9, 7) \).

### Step 1: Substitute the coordinates into the formula

\[
d = \sqrt{(9 - 3)^2 + (7 - 3)^2}
\]

### Step 2: Simplify the expressions

\[
d = \sqrt{6^2 + 4^2} = \sqrt{36 + 16}
\]

\[
d = \sqrt{52}
\]

### Step 3: Calculate the square root

\[
d \approx \sqrt{52} \approx 7.2111
\]

### Step 4: Round to the nearest tenth

\[
d \approx 7.2
\]

### Final Answer
The distance between points \( P(3, 3) \) and \( Q(9, 7) \) is approximately \( 7.2 \) units.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you find the midpoint between two points?
2. What is the distance between the points \( (0, 0) \) and \( (6, 8) \)?
3. Can you explain how the Pythagorean theorem is related to the distance formula?
4. What happens to the distance if one of the points is shifted by 2 units to the right?
5. How would you find the length of the diagonal of a rectangle using the distance formula?

**Tip:** When dealing with square roots, use a calculator to ensure accuracy, especially when rounding to specific decimal places.

Learn how to find the distance between two points using the distance formula. Step-by-step solution to calculate the distance between points P(3, 3) and Q(9, 7) to the nearest tenth. Suitable for Grades 7-9.

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