Question

Find the image of NPQ under the translation of (x,y) -> (x + 8, y + 1).

Which triangle shows the image of NPQ after the translation?

Answer 1

The image triangle NPQ is triangle KLM

Explanation:

The vertices of triangle NPQ are at:

N(-7,-6), P(-4,-3) an Q(-4,-6).

The rule for the translation is:

`(x,y)\to(x+8,y+1)`

This implies that:

`N(-7,-6)\to (-7+8,-6+1)=N'(1,-5)`

`P(-4,-3)\to (-4+8,-3+1)=P'(4,-2)`

`Q(-4,-6)\to (-4+8,-6+1)=Q'(4,-5)`

Therefore triangle N'P'Q' has vertices at N'(1,-5),P'(4,-2), and Q'(4,-5)

This coincides with K(1,-5),L(4,-2), and M(4,-5)

Hence the image triangle NPQ is triangle KLM