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To find the length of \( RS \), we can use the distance formula:

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

In this case, the coordinates of \( R \) are \( (-3, -1) \), and the coordinates of \( S \) are \( (2, 4) \). Now, applying the formula:

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

Let me calculate this for you.The length of \( RS \) is approximately \( 7.07 \) units, rounded to three significant figures.

Do you want further details or explanations?

Here are five related questions to explore:

1. How does the distance formula relate to the Pythagorean theorem?
2. What would be the length of a line between different points, say \( (1, 2) \) and \( (-2, -3) \)?
3. How do you find the midpoint between two points on a graph?
4. How does the slope between two points relate to the distance formula?
5. Can you apply this method to find the distance between points in 3D space?

**Tip:** The distance formula is derived from the Pythagorean theorem, so visualizing the right triangle formed by the points helps in understanding the process.

Work out the length of RS. Give your answer to 3 significant figures.

Learn how to calculate the distance between two points R(-3, -1) and S(2, 4) using the distance formula in coordinate geometry. This problem utilizes the Pythagorean theorem and is ideal for students in Grades 8-10. Answer rounded to three significant figures.

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