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Part 1
On a​ zip-line course, you are harnessed to a cable that travels through the treetops. You start at platform A and zip to each of the other platforms. How far do you travel from Platform B to Platform​ C? [B(-25,-20)] C(-20,10)]

To calculate the distance between two points on a coordinate plane, we can use the distance formula:

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

Given the coordinates for Platform B and Platform C:
- Platform B: \((-25, -20)\)
- Platform C: \((-20, 10)\)

Now, let's apply the formula:

\[
d = \sqrt{{(-20 - (-25))^2 + (10 - (-20))^2}}
\]

This simplifies to:

\[
d = \sqrt{{(5)^2 + (30)^2}} = \sqrt{25 + 900} = \sqrt{925}
\]

The distance is:

\[
d = \sqrt{925} \approx 30.41 \text{ units}
\]

So, the distance from Platform B to Platform C is approximately **30.41 units**.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. How do we interpret the distance formula geometrically?
2. Can the distance formula be applied in 3D space, and how?
3. What are other ways to calculate distances in different coordinate systems (e.g., polar coordinates)?
4. How do negative coordinates affect the outcome of the distance calculation?
5. Can the distance formula be used to find the midpoint between two points?

**Tip:** The distance formula is derived from the Pythagorean theorem, a fundamental concept in geometry.

On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at platform A and zip to each of the other platforms. How far do you travel from Platform B to Platform C? [B(-25,-20)] C(-20,10)]

Learn how to calculate the distance between two points, Platform B(-25, -20) and Platform C(-20, 10), using the distance formula. This step-by-step solution covers key geometry concepts and applies the Pythagorean theorem, making it suitable for students in Grades 8-10.

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