Video Transcript
The image of triangle 𝐶𝐷𝐸 is triangle 𝐶 prime 𝐷 prime 𝐸 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 to identify which diagram represents a translation of magnitude 𝐴𝐵, in the direction of the ray 𝐴𝐵. In each of the instances, we can see that 𝐴𝐵 represents a vertical translation in the upward direction by a varying amount. Using this information, we know that the triangle 𝐶 prime 𝐷 prime 𝐸 prime must have been translated above triangle 𝐶𝐷𝐸.
In options (C) and (D), we can see that triangle 𝐶𝐷𝐸 has been translated down. So, we can immediately eliminate these options. Let’s now consider the three remaining options, starting with option (A). We can see that the length of 𝐴𝐵 is seven units. So, the magnitude of the translation will be seven units in the vertically upward direction. We can check whether each of 𝐶, 𝐷, and 𝐸 map to their corresponding points after the translation. We can see that 𝐸 maps to 𝐸 prime, but 𝐶 and 𝐷 do not map to 𝐶 prime and 𝐷 prime. We can sketch the triangle 𝐶𝐷𝐸 will translate to, and we can clearly see that it is not triangle 𝐶 prime 𝐷 prime 𝐸 prime. So, option (A) is not the correct solution.
Next, looking at option (B), we can see that the length of 𝐴𝐵 is five units. So, the translation will be five units in the vertically upward direction. We can translate triangle 𝐶𝐷𝐸 upward by five units to see the result. Translating each of the points 𝐶, 𝐷, and 𝐸, we can see that they translate to 𝐶 prime, 𝐷 prime, and 𝐸 prime. Hence, when translated by magnitude 𝐴𝐵 in the direction of the ray 𝐴𝐵, triangle 𝐶𝐷𝐸 is translated to triangle 𝐶 prime 𝐷 prime 𝐸 prime. Therefore, we have that our solution to this question is option (B).
For completeness, we can check option (E). The length of 𝐴𝐵 is five units, so the translation will be of magnitude five units. We translate each of the points vertically upwards by five units. And we can see where the triangle 𝐶𝐷𝐸 translates to. Since it is not the triangle 𝐶 prime 𝐷 prime 𝐸 prime, option (E) also cannot be correct.
Overall, we have shown that the only diagram which represents the translation is option (B).
