### Using the Pythagorean Theorem to Find Distance Between Points**Problem Statement:**How can we use the Pythagorean theorem to find the length of segment AB, or in other words, the distance between A (-2,1) and B (3,3)? Find the distance between A and B.**Graph Explanation:**The graph provided is a Cartesian coordinate system with two points labeled: A at coordinates (-2, 1) and B at coordinates (3, 3). A line segment connects these two points. The x-axis and y-axis intersect at (0,0), and the grid lines help indicate the location of the points and the segments in between.**Steps to Solve:**1. **What would you do first?** - Determine the horizontal and vertical distances between the two points (A and B) on the grid. - To find the horizontal distance (change in x-coordinates), subtract the x-coordinate of A from the x-coordinate of B: \[ |3 - (-2)| = |3 + 2| = 5. \] - To find the vertical distance (change in y-coordinates), subtract the y-coordinate of A from the y-coordinate of B: \[ |3 - 1| = 2. \]2. **What would your next step be?** - Use the Pythagorean theorem to find the length of the line segment AB. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. - Here, the distance between A and B (denoted as $d$) is the hypotenuse, the horizontal change (5) and vertical change (2) are the other sides: \[ d^2 = 5^2 + 2^2. \] - Calculate the squares: \[ d^2 = 25 + 4. \] - Sum the squares: \[ d^2 = 29. \] - Take the square root of both sides to solve for $d$: \[ d = \sqrt{29}. \]3. **What is the distance between the two points?** -

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Description: ### Using the Pythagorean Theorem to Find Distance Between Points**Problem Statement:**How can we use the Pythagorean theorem to find the length of segment AB, or in other words, the distance between A (-2,1) and B (3,3)? Find the distance between A

Given: The two points are A = (-2,1) and B = (3,3) To Find: The distance between A and B

Math

Geometry

How can we use the Pythagorean theorem to find the length of segment AB, or in other words, the distance between A (-2,1) and B (3,3)? Find the distance between A and B. (3,3) (-2,1) 1) What would you do first? 2) What would your next step be? 3) What is the distance between the two points?

How can we use the Pythagorean theorem to find the length of segment AB, or in other words, the distance between A (-2,1) and B (3,3)? Find the distance between A and B. (3,3) (-2,1) 1) What would you do first? 2) What would your next step be? 3) What is the distance between the two points?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

### Using the Pythagorean Theorem to Find Distance Between Points

**Problem Statement:**
How can we use the Pythagorean theorem to find the length of segment AB, or in other words, the distance between A (-2,1) and B (3,3)? Find the distance between A and B.

**Graph Explanation:**
The graph provided is a Cartesian coordinate system with two points labeled: A at coordinates (-2, 1) and B at coordinates (3, 3). A line segment connects these two points. The x-axis and y-axis intersect at (0,0), and the grid lines help indicate the location of the points and the segments in between.

**Steps to Solve:**

1. **What would you do first?**
- Determine the horizontal and vertical distances between the two points (A and B) on the grid.
- To find the horizontal distance (change in x-coordinates), subtract the x-coordinate of A from the x-coordinate of B:
\[
|3 - (-2)| = |3 + 2| = 5.
\]
- To find the vertical distance (change in y-coordinates), subtract the y-coordinate of A from the y-coordinate of B:
\[
|3 - 1| = 2.
\]

2. **What would your next step be?**
- Use the Pythagorean theorem to find the length of the line segment AB. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
- Here, the distance between A and B (denoted as $d$) is the hypotenuse, the horizontal change (5) and vertical change (2) are the other sides:
\[
d^2 = 5^2 + 2^2.
\]
- Calculate the squares:
\[
d^2 = 25 + 4.
\]
- Sum the squares:
\[
d^2 = 29.
\]
- Take the square root of both sides to solve for $d$:
\[
d = \sqrt{29}.
\]

3. **What is the distance between the two points?**
-

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