Find the distance between the two points (5, -3) and (2, 5). Simplify your answer, and write the exact answer in simplest radical form for an irrational answer. d =
Find the distance between the two points (5, -3) and (2, 5). Simplify your answer, and write the exact answer in simplest radical form for an irrational answer. d =
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Problem Context:**
We are tasked with finding the distance between the two points \( (5, -3) \) and \( (2, 5) \).
**Instructions:**
1. **Distance Formula:**
- The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) in a 2-dimensional plane is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
2. **Apply the formula to the points \( (5, -3) \) and \( (2, 5) \):**
- Identify the coordinates: \( x_1 = 5 \), \( y_1 = -3 \), \( x_2 = 2 \), \( y_2 = 5 \).
- Substitute these values into the distance formula:
\[
d = \sqrt{(2 - 5)^2 + (5 + 3)^2}
\]
3. **Calculation:**
- Calculate each part:
\[
(2 - 5)^2 = (-3)^2 = 9
\]
\[
(5 + 3)^2 = 8^2 = 64
\]
- Add these results:
\[
9 + 64 = 73
\]
4. **Simplify:**
- The distance \( d = \sqrt{73} \).
**Conclusion:**
The exact answer, in simplest radical form, is \( \sqrt{73} \).
**Note:** This problem requires solving using the distance formula between two Cartesian coordinate points and simplifying the result into its simplest radical form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0caa6687-4e6f-4c6c-bc0f-3d83b65e20e1%2F5bcdcb97-f2e6-4c15-89fa-c41e5453a81f%2Fb0kfxms_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Context:**
We are tasked with finding the distance between the two points \( (5, -3) \) and \( (2, 5) \).
**Instructions:**
1. **Distance Formula:**
- The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) in a 2-dimensional plane is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
2. **Apply the formula to the points \( (5, -3) \) and \( (2, 5) \):**
- Identify the coordinates: \( x_1 = 5 \), \( y_1 = -3 \), \( x_2 = 2 \), \( y_2 = 5 \).
- Substitute these values into the distance formula:
\[
d = \sqrt{(2 - 5)^2 + (5 + 3)^2}
\]
3. **Calculation:**
- Calculate each part:
\[
(2 - 5)^2 = (-3)^2 = 9
\]
\[
(5 + 3)^2 = 8^2 = 64
\]
- Add these results:
\[
9 + 64 = 73
\]
4. **Simplify:**
- The distance \( d = \sqrt{73} \).
**Conclusion:**
The exact answer, in simplest radical form, is \( \sqrt{73} \).
**Note:** This problem requires solving using the distance formula between two Cartesian coordinate points and simplifying the result into its simplest radical form.
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