Question

two triangles, △ abc and △ def, have corresponding angles that are equal, and the sides of △ def are twice as long as the sides of △ abc. which transformation maps △ abc onto △ def?

○ translation only

○ rotation followed by reflection

○ dilation with scale factor 2 centered at a point

○ reflection followed by rotation

Explanation:

Step1: Recall transformation definitions

• Translation: Moves a figure without changing size/shape.
• Rotation/Reflection: Rigid transformations (preserve size/shape).
• Dilation: Changes size (scales) while preserving shape (angles equal, sides proportional).

Step2: Analyze the problem

Triangles have equal corresponding angles (similar) and sides of \( \triangle DEF \) are twice \( \triangle ABC \). So, a transformation that scales the figure by factor 2 is needed.

Step3: Evaluate options

• "Translation only": Preserves size, incorrect.
• "Rotation followed by reflection": Rigid (preserves size), incorrect.
• "Dilation with scale factor 2 centered at a point": Scales sides by 2, preserves angles (similar triangles), correct.
• "Reflection followed by rotation": Rigid (preserves size), incorrect.

Answer:

C. Dilation with scale factor 2 centered at a point