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To find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a coordinate plane, we can use the distance formula:

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

### a) Distance between \((0, 5)\) and \((2, -5)\):
- \((x_1, y_1) = (0, 5)\)
- \((x_2, y_2) = (2, -5)\)

Now, applying the distance formula:

\[
\text{Distance} = \sqrt{(2 - 0)^2 + (-5 - 5)^2} = \sqrt{2^2 + (-10)^2} = \sqrt{4 + 100} = \sqrt{104} \approx 10.2
\]

So, the distance is approximately **10.2 units**.

### b) Distance between \((-1, -3)\) and \((-3, 2)\):
- \((x_1, y_1) = (-1, -3)\)
- \((x_2, y_2) = (-3, 2)\)

Applying the distance formula:

\[
\text{Distance} = \sqrt{(-3 - (-1))^2 + (2 - (-3))^2} = \sqrt{(-3 + 1)^2 + (2 + 3)^2} = \sqrt{(-2)^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29} \approx 5.39
\]

Thus, the distance is approximately **5.39 units**.

Would you like further details or have any questions about the steps?

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Here are 5 related questions:
1. How do you calculate the midpoint between two points in the coordinate plane?
2. Can you generalize the distance formula for three-dimensional space?
3. How does the distance formula relate to the Pythagorean theorem?
4. What are the units of the calculated distance between two points?
5. How can you find the slope between two points?

**Tip:** When using the distance formula, always double-check the subtraction inside the parentheses before squaring.

Find the distance between the following two points: a) (0, 5) and (2, -5), b) (-1, -3) and (-3, 2).

Learn how to find the distance between two points on a coordinate plane using the distance formula. We solve for the points (0, 5) and (2, -5), as well as (-1, -3) and (-3, 2), applying the Pythagorean theorem. Suitable for students in Grades 7-9.

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