Question

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

A) The triangles are neither similar nor congruent.
B) The triangles are similar and congruent.
C) The triangles are similar but not congruent.
D) Triangle KLM has a smaller area.

Answer 1

When a triangle is reflected across the y-axis and then dilated by a scale factor of 3, the resulting triangles are similar but not congruent. Triangle KLM has a larger area than Triangle EFG.

Step-by-step explanation:

When a triangle is reflected across the y-axis, the x-coordinates of its vertices are negated while the y-coordinates remain the same. After the reflection, the triangle is dilated by a scale factor of 3 centered at the origin (0,0), which means that the side lengths of the triangle are multiplied by 3.

Since dilation preserves shape, the triangles are similar. However, they are not congruent because their corresponding side lengths are different. Therefore, the correct answer is C) The triangles are similar but not congruent.

Regarding the area, the area of the dilated triangle KLM will be nine times the area of the original triangle EFG because the scale factor is 3. Therefore, Triangle KLM has a larger area, not smaller.