### Graph Transformation Activity: Triangle ABC#### Original Triangle ABCThe 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 TaskBelow the initial graph, the instruction reads: **"Draw the triangle ABC using the rule (x,y) → (x+2, y-3)"**#### Blank Cartesian Plane for TransformationA 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 TransformationTo 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 TriangleUsing 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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Answered: IB C Draw the triangle ABC using the…

Math

Algebra

IB C Draw the triangle ABC using the rule (x,y) → (x+2, y-3)

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

### 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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