Question

Triangle EFG is reflected across the y-axis on a coordinate plane and then dilated by a scale factor of 3 centered at (0,0) to produce triangle KLM. What is true about triangle EFG and triangle KLM? Select all the true statements.

A. The triangles are neither similar nor congruent.
B. The triangles are similar and congruent.
C. Triangle KLM has a smaller area.
D. Triangle KLM has a larger area.
E. The area of the triangles is the same.

Answer 1

Triangle EFG, when reflected across the y-axis and then dilated by 3, results in triangle KLM being similar to EFG but with a larger area. KLM is not congruent to EFG, and their areas are not the same.

Step-by-step explanation:

When triangle EFG is reflected across the y-axis and then dilated by a scale factor of 3 centered at (0,0) to produce triangle KLM, certain properties of the triangles can be determined. The reflection across the y-axis changes the orientation of the triangle but does not affect its size or shape. The subsequent dilation by a scale factor of 3 magnifies all dimensions of the triangle by 3 times. As a result:

• The triangles are similar because they have the same shape but different sizes due to the dilation process.
• Triangle KLM has a larger area. Specifically, the area of triangle KLM will be 9 times larger than that of triangle EFG, because when a triangle is dilated by a scale factor, the area changes by the scale factor squared.

Therefore, of the provided options, B is incorrect because the triangles are not congruent (they do not have the same size). C is incorrect because triangle KLM actually has a larger area, not a smaller one. And E is also incorrect because the areas of the triangles are not the same. The correct answers are the triangles are similar (A) and triangle KLM has a larger area (D).