Video Transcript
Find the images of the points 𝐴
and 𝐵 of the line segment 𝐴𝐵 under the translation four, three.
We’re going to carry out the
translation four, three on this line segment. That means the line segment will
move four units to the right and three units up. The images of these points are the
points of 𝐴 and 𝐵 after the translation. A translation will add or subtract
constant values from the 𝑥- and 𝑦-coordinates. A translation 𝑝, 𝑞 on the point
𝑥, 𝑦 will be mapped to 𝑥 add 𝑝, 𝑦 add 𝑞.
So let’s start by carrying out this
translation graphically. We can do this by firstly
considering point 𝐴 and then point 𝐵. We move point 𝐴 four units to the
right and three units up. We denote this new point with 𝐴
prime. Now we can do the same with point
𝐵. We move point 𝐵 four units to the
right and three units up. This gives us the image of 𝐵, 𝐵
prime. We then get the translated line
segment by joining 𝐴 prime with 𝐵 prime.
We can read the images of 𝐴 and 𝐵
directly from the graph by reading the coordinates of the points 𝐴 prime and 𝐵
prime. We could also use our formal
definition to work out these points. 𝐴 is the point negative two,
negative six. We map 𝐴 to its image, 𝐴 prime,
by adding four to the 𝑥-coordinate, because that’s the horizontal translation, and
three to the 𝑦-coordinate, because that’s the vertical translation. That gives us the image 𝐴 prime is
two, negative three.
Let’s calculate 𝐵 prime. Point 𝐵 has coordinates one,
negative four. We map this to its image by adding
four to the 𝑥-coordinate and three to the 𝑦-coordinate. That gives us the image of 𝐵, 𝐵
prime, is five, negative one. We can verify these points by
checking the translation we did on the graph. And we see that the images of 𝐴
and 𝐵 are correct. So that’s our answer. The image of 𝐴 is two, negative
three, and the image of 𝐵 is five, negative one.
