options: Experiment with transformations in the plane.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Analyze, compare, create, and compose shapes.

Define trigonometric ratios and solve problems involving right triangles.

Explain volume formulas and use them to solve problems.

Understand and apply the Pythagorean Theorem.

Prove theorems involving similarity.

Find arc lengths and areas of sectors of circles.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Understand similarity in terms of similarity transformations.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Understand congruence in terms of rigid motions.

Understand and apply theorems about circles.

Classify two-dimensional figures into categories based on their properties.

Reason with shapes and their attributes.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Apply trigonometry to general triangles.

Translate between the geometric description and the equation for a conic section.

Prove geometric theorems.

Apply geometric concepts in modeling situations.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Use coordinates to prove simple geometric theorems algebraically.

Visualize relationships between two-dimensional and three-dimensional objects.

Make geometric constructions.

Solve real-world and mathematical problems involving area, surface area, and volume.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
problem_activity: Task
Suppose $f$ is the map of the plane which takes each point $(x,y)$ to the point $(x-3,y)$ and $g$ is the map of the plane that takes each $(x,y)$ to $(3x,y)$.
Below is a triangle $ABC$.
[IMG]
Show the image of $\triangle ABC$ after applying each of the maps $f$ and $g$.
Does $f$ preserve distances and angles? Explain.
Does $g$ preserve distances and angles? Explain.


correct_option_index: 0