Question
2. Find the distance between the points \[ (8,4) \text { and }(3,4) \]
Ask by Lawson Byrd. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The distance between the points \( (8, 4) \) and \( (3, 4) \) is 5 units.
Solution
To find the distance between the points \( (8, 4) \) and \( (3, 4) \), we can use the **distance formula**. The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) in the Cartesian plane is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
**Step-by-Step Solution:**
1. **Identify the coordinates:**
- First point \( (x_1, y_1) = (8, 4) \)
- Second point \( (x_2, y_2) = (3, 4) \)
2. **Plug the values into the distance formula:**
\[
d = \sqrt{(3 - 8)^2 + (4 - 4)^2}
\]
3. **Calculate the differences:**
\[
x_2 - x_1 = 3 - 8 = -5
\]
\[
y_2 - y_1 = 4 - 4 = 0
\]
4. **Square the differences:**
\[
(-5)^2 = 25
\]
\[
0^2 = 0
\]
5. **Add the squared differences:**
\[
25 + 0 = 25
\]
6. **Take the square root of the sum:**
\[
d = \sqrt{25} = 5
\]
**Conclusion:**
The distance between the points \( (8, 4) \) and \( (3, 4) \) is **5 units**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the distance between the points \( (8,4) \) and \( (3,4) \), we can use the distance formula. However, since both points share the same \( y \)-coordinate, it's simply a horizontal line segment. The distance is calculated as the absolute difference between their \( x \)-coordinates: \[ |8 - 3| = 5 \] So, the distance is \( 5 \) units. Another fun way to visualize this is by imagining a number line, where you hop from \( 3 \) to \( 8 \) in just 5 steps! No need for fancy calculations here—just a straight walk along the x-axis!
