Triangles H J K and L M N are congruent. Triangle H J K is rotated about point H to form triangle L N M. Triangle L M N is higher than triangle H J K.

Question

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

Translate H to L and rotate about H until HK lies on the line containing LM.
Translate K to M and rotate about K until HK lies on the line containing LM.
Translate K to N and rotate about K until HK lies on the line containing LN.
Translate H to N and rotate about H until HK lies on the line containing LN.

Answer 1

To map ΔHJK to ΔLMN using a translation and a rotation, we can follow these steps:

1. Translate H to L: First, we translate point H to point L. This will relocate the entire triangle so that point H coincides with point L.

2. Rotate about L: After the translation, we need to rotate triangle HJK around point L until side HK aligns with side LM. This rotation aligns the remaining parts of the triangle so that the two triangles are now properly positioned and oriented.

By following this process, you successfully map ΔHJK to ΔLMN.

Among the given options, the correct move is:

Translate H to L and rotate about H until HK lies on the line containing LM.

This method effectively uses both a translation and a rotation to achieve the desired mapping of the triangles.