https://file.aiquickdraw.com/mathbot/file/1725392403889x8pckl1d.jpg

The problem involves understanding the dilation of a triangle on a coordinate plane and analyzing the properties of the original and dilated triangles.

### Given:
- **Triangle \( \Delta A'B'C' \)** is the result of dilating **\( \Delta ABC \)** about point **\( P \)** with a scale factor of 3.
- The task is to determine whether certain claims about the properties of **\( \Delta ABC \)** and **\( \Delta A'B'C' \)** are true or false.

### Claims to Analyze:
1. **\( AB = A'B' \)** after dilation.
2. **\( \angle ABC = \angle A'B'C' \)** after dilation.

### Analyzing the Claims:
1. **Claim: \( AB = A'B' \)** is False.**
   - A dilation with a scale factor other than 1 changes the lengths of the sides of the triangle. Since the scale factor is 3, every side of \( \Delta A'B'C' \) will be 3 times longer than the corresponding side in \( \Delta ABC \). Therefore, \( AB \) is not equal to \( A'B' \).

2. **Claim: \( \angle ABC = \angle A'B'C' \)** is True.**
   - Dilation preserves the angles of the original figure. Therefore, the angles of \( \Delta ABC \) will be equal to the corresponding angles in \( \Delta A'B'C' \).

### Conclusion:
- The first claim \( AB = A'B' \) is **False**.
- The second claim \( \angle ABC = \angle A'B'C' \) is **True**.

Would you like more details, or do you have any questions?

---

**Relative Questions:**
1. How does the location of the point \( P \) affect the dilation?
2. What happens to the area of the triangle \( \Delta A'B'C' \) compared to \( \Delta ABC \) when the scale factor is 3?
3. If the scale factor were 1, what would happen to the sides and angles of the triangle after dilation?
4. How would a negative scale factor affect the triangle?
5. Can dilation result in a congruent triangle under certain conditions?

**Tip:** Always remember that dilation changes the size of a figure but preserves the shape, meaning angles remain the same while side lengths are scaled by the dilation factor.

Triangle ΔA'B'C' is the result of dilating ΔABC about point P by a scale factor of 3. Determine whether each claim about the properties of ΔABC and ΔA'B'C' is true or false: 1. AB = A'B' after dilation. 2. ∠ABC = ∠A'B'C' after dilation.

Learn how to analyze the properties of triangles after dilation with a scale factor. This problem covers key concepts like dilation, angle preservation, and proportionality of sides, 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