Give me some visual problems is translating, reflecting, rotations and dialating something across a graph

Here are some visual problems that involve translating, reflecting, rotating, and dilating objects across a graph. Each problem is described step-by-step for you to visualize or draw on a graph.

### Problem 1: Translation
1. **Original Object**: Consider a triangle with vertices at \( A(1, 2) \), \( B(3, 4) \), and \( C(2, 6) \).
2. **Task**: Translate the triangle 4 units to the right and 3 units down.
3. **Question**: What are the new coordinates of the vertices after the translation?

### Problem 2: Reflection
1. **Original Object**: Consider a square with vertices at \( P(-2, 3) \), \( Q(1, 3) \), \( R(1, 6) \), and \( S(-2, 6) \).
2. **Task**: Reflect the square across the y-axis.
3. **Question**: What are the new coordinates of the vertices after the reflection?

### Problem 3: Rotation
1. **Original Object**: Consider a line segment with endpoints at \( M(2, 1) \) and \( N(5, 1) \).
2. **Task**: Rotate the line segment 90° counterclockwise around the origin.
3. **Question**: What are the new coordinates of the endpoints after the rotation?

### Problem 4: Dilation
1. **Original Object**: Consider a rectangle with vertices at \( J(1, 1) \), \( K(4, 1) \), \( L(4, 3) \), and \( M(1, 3) \).
2. **Task**: Dilate the rectangle by a scale factor of 2 with the origin as the center of dilation.
3. **Question**: What are the new coordinates of the vertices after the dilation?

### Problem 5: Combination of Transformations
1. **Original Object**: Consider a parallelogram with vertices at \( X(-3, 2) \), \( Y(-1, 4) \), \( Z(1, 2) \), and \( W(-1, 0) \).
2. **Task**: Reflect the parallelogram across the x-axis, and then translate it 2 units to the left.
3. **Question**: What are the new coordinates of the vertices after both transformations?

---

### Would you like detailed solutions for any of these problems or have any questions?

### Relative Questions:
1. How do you determine the new coordinates after a translation?
2. What is the effect of reflecting an object across the x-axis versus the y-axis?
3. How does the angle of rotation affect the coordinates of a shape on a graph?
4. What happens to the size and position of a shape when it is dilated by a factor of less than 1?
5. Can you combine more than two transformations, and how would that affect the final result?

### Tip: When performing a transformation, always track each vertex of the shape individually to ensure accuracy in your final result.

Give me some visual problems is translating, reflecting, rotations and dialating something across a graph.

Explore a variety of problems involving translating, reflecting, rotating, and dilating objects across a graph. Learn key geometry concepts such as translation formulas, reflection rules, rotation angles, and dilation scaling factors. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation