Question

once you have completed the above problems and checked your solutions, complete the lesson checkpoint below. complete the lesson reflection above by circling your current understanding of the learning goal. 1. complete the following △qrs is the image of △lmn under a sequence of transformations. can each of the following sequences be used to create the image, △qrs, from the pre - image, △lmn? select yes or no. a. reflect across the y - axis and then translate along the vector ⟨0,−4⟩. b. translate along the vector ⟨0,−4⟩ and then reflect across the y - axis. c. rotate 90° clockwise about the origin, reflect across the x - axis, and then rotate 90° counterclockwise about the origin. d. rotate 180° about the origin, reflect across the x - axis, and then translate along the vector ⟨0,−4⟩.

Explanation:

Step1: Analyze transformation in a

Reflecting across y - axis changes sign of x - coordinates. Translating along $\langle0, - 4
angle$ moves figure 4 units down. By observing the orientation and position of $\triangle LMN$ and $\triangle QRS$, this sequence can work.

Step2: Analyze transformation in b

Translating first and then reflecting across y - axis will change the relative position of the figure in a way that does not match $\triangle QRS$ from $\triangle LMN$.

Step3: Analyze transformation in c

Rotating 90° clockwise about origin, reflecting across x - axis and then rotating 90° counter - clockwise about origin will not result in the correct orientation and position of $\triangle QRS$.

Step4: Analyze transformation in d

Rotating 180° about origin, reflecting across x - axis and then translating along $\langle0, - 4
angle$ will not give the correct image $\triangle QRS$.

Answer:

a. Yes
b. No
c. No
d. No