Question
Find the distance from the point \( (6,3) \) to the line \( x=5 \)
Ask by Hodges Burgess. in the United States
Jan 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The distance from the point \( (6, 3) \) to the line \( x = 5 \) is **1 unit**.
Solution
To find the distance between the point \( (6, 3) \) and the line \( x = 5 \), we can use the following approach:
1. **Understand the Geometry**:
- The line \( x = 5 \) is a **vertical line** that passes through all points where the \( x \)-coordinate is 5.
- The point \( (6, 3) \) has an \( x \)-coordinate of 6.
2. **Calculate the Distance**:
- Since the line is vertical, the shortest distance between the point and the line is the horizontal (left-right) distance.
- This distance is simply the absolute difference between the \( x \)-coordinates of the point and the line.
\[
\text{Distance} = |6 - 5| = 1
\]
So, the distance from the point \( (6, 3) \) to the line \( x = 5 \) is **1 unit**.
**Answer:** 1
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Simplify this solution Beyond the Answer
To find the distance from the point \( (6,3) \) to the line \( x=5 \), we can simply look at the horizontal distance between the point and the vertical line. The line \( x=5 \) is vertical, meaning it has a constant x-coordinate of 5. The x-coordinate of the point \( (6,3) \) is 6, so the distance between the point and the line is calculated as follows: \[ \text{Distance} = |x_1 - x_2| = |6 - 5| = 1 \] Thus, the distance from the point \( (6,3) \) to the line \( x=5 \) is \( 1 \) unit.
