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To find the distance from point \( A(3, 0) \) to line \( XZ \), we can use the formula to find the distance from a point to a line:

\[
d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}
\]

Here, the line \( XZ \) is formed by points \( X(-1, -2) \) and \( Z(2, 7) \). First, let's find the equation of the line \( XZ \).

1. **Slope of the line \( XZ \)**:  
   The slope \( m \) is given by:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - (-2)}{2 - (-1)} = \frac{9}{3} = 3
   \]

2. **Equation of the line \( XZ \)**:  
   Using the point-slope form of a line \( y - y_1 = m(x - x_1) \), where \( m = 3 \) and \( (x_1, y_1) = (-1, -2) \):
   \[
   y - (-2) = 3(x - (-1))
   \]
   Simplifying:
   \[
   y + 2 = 3(x + 1)
   \]
   \[
   y + 2 = 3x + 3
   \]
   \[
   y = 3x + 1
   \]
   So, the equation of the line \( XZ \) is \( y = 3x + 1 \), or in standard form, \( 3x - y + 1 = 0 \).

3. **Distance from point \( A(3, 0) \) to line \( 3x - y + 1 = 0 \)**:
   Using the formula:
   \[
   d = \frac{|3(3) - 1(0) + 1|}{\sqrt{3^2 + (-1)^2}} = \frac{|9 + 1|}{\sqrt{9 + 1}} = \frac{10}{\sqrt{10}} = \sqrt{10}
   \]
   Approximating:
   \[
   d \approx 3.2 \text{ units}
   \]

Thus, the distance from point \( A \) to line \( XZ \) is approximately **3.2 units**.

Would you like more details on any step or have any questions?

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Here are 5 related questions you might find interesting:

1. How do you find the equation of a line using different forms (slope-intercept, point-slope)?
2. What is the geometric interpretation of the distance from a point to a line?
3. Can the distance formula be applied in three-dimensional space?
4. How do you find the midpoint of a line segment between two points?
5. How can the slope help determine if two lines are parallel or perpendicular?

**Tip:** Always convert the line equation to standard form \( Ax + By + C = 0 \) when using the distance formula!

Find the distance from point A to line XZ. Round your answer to the nearest tenth.

Learn how to calculate the distance from point A(3,0) to the line XZ using the formula for point-to-line distance. This problem covers key concepts in coordinate geometry, including slope calculation and distance formulas.

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