Triangles H J K and L M N are shown. The triangles have identical side lengths and angle measures. Triangle H J K is slightly lower and to the left of triangle L M N. Triangle H J K is reflected to form triangle L M N.

How can a translation and a reflection be used to map ΔHJK to ΔLMN?

Translate K to N and reflect across the line containing HJ.
Translate K to N and reflect across the line containing JK.
Translate H to L and reflect across the line containing JK.
Translate K to L and reflect across the line containing HJ.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To map triangle ΔHJK to triangle ΔLMN using a translation followed by a reflection, we first need to observe the relationship between the two triangles.

  1. Translation: We should first translate one of the points of triangle HJK to the corresponding point in triangle LMN. In this case, one effective way is to translate point K to point N.

  2. Reflection: After translating point K to point N, we can reflect the entire triangle across the appropriate line to get the final position of triangle LMN. The logical line to reflect across would be the line that contains segment HJ.

So, the correct sequence is:

  • Translate K to N and then
  • Reflect across the line containing HJ.

Therefore, the answer is: Translate K to N and reflect across the line containing HJ.