https://file.aiquickdraw.com/mathbot/file/1729256199512270bndu0.jpg

To solve Question 7 from the image, we need to describe the transformations between different triangles shown on the Cartesian plane, based on geometric transformations like reflection, rotation, translation, or dilation.

Let's break down the transformations for each pair of triangles:

### 7.1. \( \triangle ABC \) to \( \triangle A'B'C' \)
This appears to be a **reflection** across the y-axis. The coordinates of the triangle's points have been mirrored, with \( A \) becoming \( A' \), \( B \) becoming \( B' \), and \( C \) becoming \( C' \).

### 7.2. \( \triangle A'B'C' \) to \( \triangle DEF \)
This transformation seems to be a **translation**. Triangle \( A'B'C' \) is moved downwards and slightly to the right to form \( \triangle DEF \).

### 7.3. \( \triangle A'B'C' \) to \( \triangle JKL \)
This transformation looks like a **rotation** by 180° around the origin. The points of \( \triangle A'B'C' \) rotate to match the positions of \( \triangle JKL \).

### 7.4. \( \triangle A'B'C' \) to \( \triangle GHI \)
This transformation involves a **rotation** of 90° counterclockwise around the origin.

### 7.5. \( \triangle MNP \) to \( \triangle M'N'P' \)
This is a **reflection** across the x-axis. The triangle \( \triangle MNP \) is mirrored with respect to the x-axis, resulting in \( \triangle M'N'P' \).

### 7.6. \( \triangle MNP \) to \( \triangle QRS \)
This transformation appears to be a **translation**. The triangle is shifted upwards and to the right to form \( \triangle QRS \).

### 7.7. \( \triangle TUV \) to \( \triangle MNP \)
This looks like a **translation** as well, where \( \triangle TUV \) is moved downward to align with \( \triangle MNP \).

### 7.8. \( \triangle TUV \) to \( \triangle WXY \)
This appears to be a **reflection** across the y-axis. The coordinates of \( \triangle TUV \) are reflected, resulting in \( \triangle WXY \).

These are the transformations described between the pairs of triangles.

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Do you want details or have any questions on this? Here are 5 related questions to explore further:

1. What is the general rule for reflecting a point across the y-axis?
2. How do you calculate the coordinates of a point after a 90° counterclockwise rotation around the origin?
3. What is the difference between a translation and a reflection?
4. How do you verify if a transformation is a reflection or a rotation based on coordinates?
5. What would happen if you combined a reflection and rotation? How does the outcome compare to a single transformation?

**Tip**: When identifying geometric transformations, pay close attention to the coordinates of key points and how they change between figures.

Describe the transformations between the triangles on the Cartesian plane as shown in the image. The triangles are labeled as ΔABC, ΔA'B'C', ΔDEF, ΔGHI, ΔJKL, ΔMNP, ΔM'N'P', ΔQRS, ΔTUV, and ΔWXY.

This problem involves describing various geometric transformations, including reflections, rotations, and translations, between triangles on a Cartesian plane. Key concepts include reflections across the axes, rotations about the origin, and translations. The problem is suitable for students in Grades 10-12 studying geometric transformations.

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