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We need to calculate the total distance Rhea traveled from point \( K(2, 2) \) to point \( L(-1, 6) \), and then to point \( M(-4, 2) \) using the coordinate plane.

1. **Distance from K to L**:
   The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the distance formula:
   \[
   d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   Substituting the coordinates of \( K(2, 2) \) and \( L(-1, 6) \):
   \[
   d(KL) = \sqrt{(-1 - 2)^2 + (6 - 2)^2} = \sqrt{(-3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{km}
   \]

2. **Distance from L to M**:
   Using the same formula, substituting the coordinates of \( L(-1, 6) \) and \( M(-4, 2) \):
   \[
   d(LM) = \sqrt{(-4 - (-1))^2 + (2 - 6)^2} = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{km}
   \]

3. **Total distance**:
   The total distance traveled is the sum of the two distances:
   \[
   \text{Total distance} = 5 \, \text{km} + 5 \, \text{km} = 10 \, \text{km}
   \]

Therefore, the total distance Rhea traveled is **10 kilometers**.

Would you like any further details or clarifications?

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Here are 5 related questions you might find interesting:
1. What is the formula for the midpoint between two points on a coordinate plane?
2. How would the distance change if each unit represented 2 kilometers instead of 1?
3. What would the total distance be if Rhea also traveled from point \( M \) back to \( K \)?
4. How can we calculate the area of the triangle formed by points \( K \), \( L \), and \( M \)?
5. What is the slope of the line connecting points \( K \) and \( L \)?

**Tip**: When working with the distance formula, always ensure that signs are handled carefully when subtracting the coordinates!

Rhea is using a coordinate grid to map out how far she biked from each place in town. If each unit on the grid represents 1 kilometer, the distance Rhea traveled from point K to point L to point M is _____ km. Round to the nearest kilometer, if necessary.

Learn how to calculate the distance Rhea biked between points K(2, 2), L(-1, 6), and M(-4, 2) on a coordinate grid using the distance formula. This problem covers key concepts in coordinate geometry, including calculating the distance between two points. Suitable for students in Grades 7-9.

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