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To find the distance from point \( A \) to the line \( \overline{XZ} \), we will use the formula for the distance from a point to a line. First, we need to determine the equation of line \( \overline{XZ} \).

### Step 1: Finding the Equation of \( \overline{XZ} \)

The coordinates of points \( X \) and \( Z \) are:
- \( X(-4, -3) \)
- \( Z(4, -1) \)

The slope of \( \overline{XZ} \) is calculated as:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-3)}{4 - (-4)} = \frac{-1 + 3}{4 + 4} = \frac{2}{8} = \frac{1}{4}
\]

Using point \( X(-4, -3) \) and the slope \( m = \frac{1}{4} \), the equation of line \( \overline{XZ} \) can be written in point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Substitute \( y_1 = -3 \), \( x_1 = -4 \), and \( m = \frac{1}{4} \):
\[
y + 3 = \frac{1}{4}(x + 4)
\]
Simplifying:
\[
y = \frac{1}{4}x + 1 - 3 \quad \Rightarrow \quad y = \frac{1}{4}x - 2
\]

The equation of \( \overline{XZ} \) is:
\[
y = \frac{1}{4}x - 2
\]

### Step 2: Using the Point-to-Line Distance Formula

The formula for the distance from a point \( (x_1, y_1) \) to a line \( Ax + By + C = 0 \) is:
\[
d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}
\]

Rewriting the line \( y = \frac{1}{4}x - 2 \) in standard form \( Ax + By + C = 0 \):
\[
\frac{1}{4}x - y - 2 = 0 \quad \Rightarrow \quad x - 4y - 8 = 0
\]
So, \( A = 1 \), \( B = -4 \), and \( C = -8 \).

Point \( A \) has coordinates \( (3, 3) \).

Substitute into the formula:
\[
d = \frac{|1 \cdot 3 - 4 \cdot 3 - 8|}{\sqrt{1^2 + (-4)^2}} = \frac{|3 - 12 - 8|}{\sqrt{1 + 16}} = \frac{|-17|}{\sqrt{17}} = \frac{17}{\sqrt{17}} = \sqrt{17}
\]

### Step 3: Calculating \( \sqrt{17} \)

Approximating \( \sqrt{17} \) to the nearest tenth:
\[
\sqrt{17} \approx 4.1
\]

Therefore, the distance from point \( A \) to line \( \overline{XZ} \) is approximately **4.1 units**.

If you have any questions or want additional details, let me know! Here are 5 related questions for further practice:

1. What is the distance from point \( (2, -1) \) to the line \( y = \frac{3}{2}x + 1 \)?
2. How would you find the distance between two parallel lines?
3. What is the distance from point \( (-2, 5) \) to the x-axis?
4. Can you derive the formula for the distance from a point to a line?
5. How do you find the shortest distance between two skew lines in 3D space?

**Tip:** When finding the distance from a point to a line, always express the line equation in standard form \( Ax + By + C = 0 \) to make calculations easier.

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, 3) to the line XZ with coordinates X(-4, -3) and Z(4, -1). This detailed solution includes finding the equation of the line, using the point-to-line distance formula, and rounding the answer to the nearest tenth.

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