Video Transcript
Fill in the blank. In the figure, 𝐴𝐵𝐶𝐷 is a
square, where all interior squares are congruent and 𝐴𝑀 is equal to one
centimeter. Then, the image of the line
segment 𝐻𝑌 by a translation of magnitude two centimeters in the direction of
the ray 𝐿𝐵 is what.
To start with, the line segment
𝐻𝑌 is this one here and the ray 𝐿𝐵 is this ray here. Translating a line segment is
equivalent to translating its endpoints, in this case 𝐻 and 𝑌, and then
connecting the images of these points with a new line segment. This means we can answer this
question by finding the images of the endpoints of this line segment under the
translation.
All of the squares are
congruent and have a side length of one centimeter. The sides of the squares in the
left-to-right direction are also parallel. Therefore, the translation of
magnitude two centimeters in the direction of the ray 𝐿𝐵 is equivalent to the
ray 𝐻𝐸. Therefore, the image of 𝐻
under the translation 𝐻 prime is the point 𝐸. Similarly, the image of the
point 𝑌 under the translation 𝑌 prime is the point 𝑁. Therefore, the image of the
line segment 𝐻𝑌 by a translation of magnitude two centimeters in the direction
of the ray 𝐿𝐵 is the line segment 𝐸𝑁.
