Directions: Given triangle ABC with vertices (-8,2), (-2,2), and (-2, 8), create triangle DEF in quadrant one that uses a translation, rotation, and reflection (in any order) to take that triangle to triangle ABC and show congruence.

### Hint

How can you use the image to find the pre-image?

### Answer

One solution would be:

Triangle DEF with vertices (1, 1), (7, 1), and (7, 7).

1. 90° rotation clockwise

2. Reflection across the Y axis

3. A translation of (x-1, y+9)

Triangle DEF with vertices (1, 1), (7, 1), and (7, 7).

1. 90° rotation clockwise

2. Reflection across the Y axis

3. A translation of (x-1, y+9)

There are many solutions.

Source: Jon Henderson

Does Triangle ABC have to map sequentially onto DEF…ie, Does A have to map to D, B to E, and C to F? OR not necessarily…just has to correctly be mapped onto the preimage to show congruence with any order of points?

I love using open ended tasks in my classroom. I think this is a good one that I will use after students have learned about reflections, rotations and translations to assess students understanding. I will have them work in pairs and provide graph paper, rulers and patty paper. I will add an exit ticket on Canvas or paper where students will need to describe why the transformations worked and what properties exist in the triangle that allow us to move it and maintain congruence.

Also, to make sure I understand students draw DEF in quadrant one and then translate, rotate and reflect that triangle onto ABC correct? That is how I read it but it was a little confusing so just wanted to make sure.

This is an interesting question! I think that is definitely one way to do it, but I think students could also perform whatever translation, rotation, and reflection they want on ABC and then use the resulting triangle as their answer and assign D, E, and F accordingly.