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To find the distance between points \( X(-3, 8) \) and \( Z(-5, 1) \), we can use the distance formula:

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

Given that:

\[
X(-3, 8) = (x_1, y_1), \quad Z(-5, 1) = (x_2, y_2)
\]

Substituting into the distance formula:

\[
d = \sqrt{((-5) - (-3))^2 + (1 - 8)^2}
\]

Let's calculate this step by step.

\[
d = \sqrt{(-5 + 3)^2 + (1 - 8)^2} = \sqrt{(-2)^2 + (-7)^2}
\]

\[
d = \sqrt{4 + 49} = \sqrt{53} \approx 7.3 \, \text{units}
\]

Thus, the distance between the two points is approximately **7.3 units**.

Do you have any questions or would you like more details?

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Here are five related questions for further exploration:
1. How would you calculate the distance in 3D space between two points?
2. What is the midpoint between points \( X(-3, 8) \) and \( Z(-5, 1) \)?
3. How does the Pythagorean theorem relate to the distance formula?
4. If the coordinates of \( Z \) changed, how would the distance calculation change?
5. How can we apply the distance formula to solve real-world problems?

**Tip:** When using the distance formula, be careful with signs when subtracting the coordinates to avoid errors in squaring.

Find the distance between X(-3, 8) and Z(-5, 1). Round to the nearest tenth, if necessary.

Learn how to calculate the distance between two points, X(-3, 8) and Z(-5, 1), using the distance formula. This problem involves key concepts from coordinate geometry and applies the Pythagorean theorem. Suitable for students in Grades 9-10.

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