Question

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

Answer 1

The correct answer is the third answer Translate K to N and rotate about K until HK lies on the line containing LN.

HOPE IT HELPED °ω°

Answer 2

you need to make sure at least one point is on the correct point of the other triangle so H on L, J on M or K on N

so the second and forth won't work

now you have the 1st or 3rd to choose

 then  you need to look at the lines, the one that would work is the 3rd option:

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