MATH SOLVE

5 months ago

Q:
# △QRS is mapped to △Q'R'S' using the rules (x, y)→(−x, y) followed by (x, y)→(x−1, y+2) .Which statement describes the relationship between △QRS and △Q'R'S'?△QRS is congruent to △Q'R'S' because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.△QRS is not congruent to △Q'R'S' because the rules do not represent a sequence of rigid motions.△QRS is congruent to △Q'R'S' because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.△QRS is congruent to △Q'R'S' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions.

Accepted Solution

A:

â–łQRS is congruent to â–łQ'R'S' because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.
The transformation (x, y)â†’(â’x, y) is a reflection across the x-axis.
The transformation (x, y)â†’(xâ’1, y+2) is a translation.
No scaling or skewing is being performed. With that in mind, let's look at the options.
â–łQRS is congruent to â–łQ'R'S' because the rules represent a reflection followed by a translation, which is a sequence of rigid motions.
* Not much to say. It's completely true. So this is the correct choice.
â–łQRS is not congruent to â–łQ'R'S' because the rules do not represent a sequence of rigid motions.
* The rigid motions are translation, rotation, reflection, and glide reflection (which is a special case of reflection followed by a very specific translation). We performed only a reflection and a translation, which are both rigid motions. So this choice is a bad one.
â–łQRS is congruent to â–łQ'R'S' because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.
* We didn't perform a rotation. So this is a bad choice.
â–łQRS is congruent to â–łQ'R'S' because the rules represent a translation followed by a rotation, which is a sequence of rigid motions.
* We performed a reflection, followed by a translation. So once again, a bad choice.