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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![### Graph Transformation Activity: Triangle ABC
#### Original Triangle ABC
The first graph displays a right-angled triangle labeled \( \triangle ABC \) plotted on a Cartesian plane. The coordinates for points A, B, and C appear as follows:
- Point \( A \) is located at the origin \((0, 0)\).
- Point \( B \) is at coordinates \((4, 5)\).
- Point \( C \) is at coordinates \((3, 1)\).
Each grid unit is equivalent to 1 on both the x-axis and y-axis. The axes intersect at the origin, with positive x-values extending to the right and positive y-values extending upwards.
#### Transformation Task
Below the initial graph, the instruction reads:
**"Draw the triangle ABC using the rule (x,y) → (x+2, y-3)"**
#### Blank Cartesian Plane for Transformation
A blank Cartesian plane is provided for students to apply the given transformation rule to triangle \( \triangle ABC \).
The transformation rule \((x, y) \rightarrow (x+2, y-3)\) indicates that each point on the triangle should be moved as follows:
- Each x-coordinate should be increased by 2 units.
- Each y-coordinate should be decreased by 3 units.
#### Applying the Transformation
To apply this transformation:
1. **Point A**:
- Original coordinates: \((0, 0)\)
- Transformed coordinates: \((0+2, 0-3) = (2, -3)\)
2. **Point B**:
- Original coordinates: \((4, 5)\)
- Transformed coordinates: \((4+2, 5-3) = (6, 2)\)
3. **Point C**:
- Original coordinates: \((3, 1)\)
- Transformed coordinates: \((3+2, 1-3) = (5, -2)\)
#### Graphing the Transformed Triangle
Using the blank Cartesian plane, plot the new coordinates:
- Point A at \((2, -3)\)
- Point B at \((6, 2)\)
- Point C at \((5, -2)\)
Draw lines to connect these points and form the transformed triangle \( \triangle A'B'C' \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4788b2f4-63d1-4ed5-a5b8-64e12d009eb9%2F9f0b46b2-a22d-4643-989a-0a13549563c5%2F4cnckd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graph Transformation Activity: Triangle ABC
#### Original Triangle ABC
The first graph displays a right-angled triangle labeled \( \triangle ABC \) plotted on a Cartesian plane. The coordinates for points A, B, and C appear as follows:
- Point \( A \) is located at the origin \((0, 0)\).
- Point \( B \) is at coordinates \((4, 5)\).
- Point \( C \) is at coordinates \((3, 1)\).
Each grid unit is equivalent to 1 on both the x-axis and y-axis. The axes intersect at the origin, with positive x-values extending to the right and positive y-values extending upwards.
#### Transformation Task
Below the initial graph, the instruction reads:
**"Draw the triangle ABC using the rule (x,y) → (x+2, y-3)"**
#### Blank Cartesian Plane for Transformation
A blank Cartesian plane is provided for students to apply the given transformation rule to triangle \( \triangle ABC \).
The transformation rule \((x, y) \rightarrow (x+2, y-3)\) indicates that each point on the triangle should be moved as follows:
- Each x-coordinate should be increased by 2 units.
- Each y-coordinate should be decreased by 3 units.
#### Applying the Transformation
To apply this transformation:
1. **Point A**:
- Original coordinates: \((0, 0)\)
- Transformed coordinates: \((0+2, 0-3) = (2, -3)\)
2. **Point B**:
- Original coordinates: \((4, 5)\)
- Transformed coordinates: \((4+2, 5-3) = (6, 2)\)
3. **Point C**:
- Original coordinates: \((3, 1)\)
- Transformed coordinates: \((3+2, 1-3) = (5, -2)\)
#### Graphing the Transformed Triangle
Using the blank Cartesian plane, plot the new coordinates:
- Point A at \((2, -3)\)
- Point B at \((6, 2)\)
- Point C at \((5, -2)\)
Draw lines to connect these points and form the transformed triangle \( \triangle A'B'C' \).
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