What is the distance, to the nearest tenth, between the points (4, 3) and (9, 5)?
 

To find the distance between the points \((4, 3)\) and \((9, 5)\), we can use the distance formula:

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

Given points:
- \((x_1, y_1) = (4, 3)\)
- \((x_2, y_2) = (9, 5)\)

Plugging in the values:

\[
d = \sqrt{(9 - 4)^2 + (5 - 3)^2} = \sqrt{5^2 + 2^2} = \sqrt{25 + 4} = \sqrt{29}
\]

Now, approximate \(\sqrt{29}\):

\[
\sqrt{29} \approx 5.385
\]

Rounding to the nearest tenth:

\[
d \approx 5.4
\]

So, the distance between the points \((4, 3)\) and \((9, 5)\) is approximately **5.4** units.

Would you like to explore further details or concepts related to this problem?

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Here are 5 related questions:
1. How do you determine the midpoint between two points?
2. What is the equation of a circle with a center at \((4, 3)\) and radius equal to the distance calculated?
3. How can you calculate the slope of the line passing through these two points?
4. What would be the distance if one of the points was \((0, 0)\)?
5. How can you use the distance formula to verify if three points are collinear?

**Tip**: Always double-check your calculations, especially when dealing with square roots, to ensure accuracy when rounding.

Learn how to calculate the distance between the points (4, 3) and (9, 5) using the distance formula. This problem involves basic coordinate geometry and square root calculations. Suitable for students in Grades 7-9.

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