Question Video: Identifying a Translation Mathematics

Video Transcript

The image of 𝐶𝐸𝐹𝐷 is 𝐶 prime 𝐸 prime 𝐹 prime 𝐷 prime following a translation of magnitude 𝐴𝐵 in the direction of the ray 𝐴𝐵. Which of the following diagrams represents this?

In this question, we have a translation of magnitude 𝐴𝐵, in the direction of the ray 𝐴𝐵. Looking at the direction of the ray 𝐴𝐵 in each of the options, we can see that it is a horizontal ray, pointing towards the right. This means that the translation must move 𝐶𝐸𝐹𝐷 horizontally to the right.

If we consider the options we have, we can see that 𝐶𝐸𝐹𝐷 has been translated to the left in both options (A) and (C). Therefore, we can eliminate these two options. We should now consider the other three options. In option (B), the length of 𝐴𝐵 is 10 units. So, the magnitude of the translation will also be 10 units. We can now try translating the points 𝐶, 𝐸, 𝐹, and 𝐷 10 units to the right. We can see that the image of 𝐶𝐸𝐹𝐷 does not align with 𝐶 prime 𝐸 prime 𝐹 prime 𝐷 prime. We can add the outline of the image. And this confirms that this option cannot be correct. So, we can eliminate this option.

Moving on to option (D), we have that the length of 𝐴𝐵 is eight units. So, the magnitude of the translation will also be eight units. We can find the image of 𝐶𝐸𝐹𝐷 by translating each of the points to the right by eight units. The image of the points 𝐶, 𝐸, 𝐹, and 𝐷 line up with the points 𝐶 prime, 𝐸 prime, 𝐹 prime, and 𝐷 prime. Joining the points, we can see that 𝐷 must be our solution.

Although we have found our solution, we should still check the final option to validate our answer. We have that the length 𝐴𝐵 is eight units. So, this will also be the magnitude of the translation. We can translate each of the points eight units to the right. After the translation, we can see that three of the points line up with 𝐶 prime, 𝐸 prime, and 𝐹 prime. However, the image of the point 𝐷 does not align with 𝐷 prime. So, this option must be wrong. This confirms our solution of option (D).