To find the distance between the points [tex]\((10, 4)\)[/tex] and [tex]\((-6, 4)\)[/tex], we need to calculate the horizontal distance between them, as their vertical coordinates are the same.
### Step-by-Step Solution:
1. Identify the Horizontal Coordinates:
- The first point [tex]\((10, 4)\)[/tex] has a horizontal coordinate of [tex]\(10\)[/tex].
- The second point [tex]\((-6, 4)\)[/tex] has a horizontal coordinate of [tex]\(-6\)[/tex].
2. Calculate the Horizontal Distance:
- The distance between the horizontal coordinates [tex]\(10\)[/tex] and [tex]\(-6\)[/tex] is given by the absolute difference between these two coordinates.
- The expression to compute this horizontal distance is [tex]\(|10 - (-6)|\)[/tex].
3. Simplify the Expression in Absolute Values:
- Simplify the difference inside the absolute value: [tex]\(10 - (-6)\)[/tex] becomes [tex]\(10 + 6\)[/tex].
- Therefore, the distance is [tex]\(|10 + 6|\)[/tex].
4. Absolute Values and Summing Up:
- The absolute values are: [tex]\(|10| = 10\)[/tex] and [tex]\(|-6| = 6\)[/tex].
- Therefore, [tex]\(|10 + 6|\)[/tex] can be rewritten as [tex]\(|10| + |-6|\)[/tex].
5. Verify the Expression:
- According to our method, the distance is computed using the expression [tex]\(|10| + |-6|\)[/tex].
Thus, the correct expression that helps you find the distance between the points [tex]\((10, 4)\)[/tex] and [tex]\((-6, 4)\)[/tex] is:
[tex]\[
|10| + |-6|
\][/tex]
