### Video Transcript

The image of the line segment

𝐶𝐷 is the line segment 𝐶 prime 𝐷 prime following a translation of magnitude

𝐴𝐵 in the direction of the ray 𝐴𝐵. Which of the following diagrams

represents this?

We can approach this problem

with a process of elimination. Recall that translating a line

segment is equivalent to translating its endpoints, in this case 𝐶 and 𝐷, to

their images 𝐶 prime and 𝐷 prime and connecting the images of the points with

a new line segment. In all five diagrams, the ray

𝐴𝐵 is pointing up and to the left. So any translation of the line

segment that doesn’t place the image in this direction must be incorrect. This immediately rules out

answers (A) and (B).

Next, the translation is of

magnitude 𝐴𝐵, meaning the distance between one endpoint of the line segment

and its image must be the length 𝐴𝐵. In answer (D), the distance

between the points 𝐶 and its image 𝐶 prime is clearly less than the length

𝐴𝐵. So the answer cannot be

(D).

And finally translations leave

the lengths of line segments unchanged. And in answer (E), we can see

that the length of the image line segment 𝐶 prime 𝐷 prime is greater than the

length of the original line segment 𝐶𝐷. Therefore, the answer cannot be

(E).

Therefore, the only remaining

answer is (C). And we can see that the line

segment is indeed translated in the correct direction by the correct distance

and does not affect the size and orientation of the line.

We can check if this is correct

by constructing the translation. We’ve cleared the incorrect

answers to give some space. Taking the line segment 𝐶𝐷,

we construct two rays in the same direction as the ray 𝐴𝐵, one starting at 𝐶

and the other starting at 𝐷. Next, we set the radius of a

compass equal to the length 𝐴𝐵 and trace circles centered at 𝐶 and 𝐷. We label the points of

intersection between the circles and the rays 𝐶 prime and 𝐷 prime. 𝐶 prime and 𝐷 prime are a

distance 𝐴𝐵 from 𝐶 and 𝐷, respectively, and in the direction of the ray

𝐴𝐵. So they are the images of 𝐶

and 𝐷 under the translation. Therefore, the line segment

joining the points 𝐶 prime and 𝐷 prime is the image of the line segment 𝐶𝐷

under the translation. And this matches visually with

option (C).