Question

A segment has endpoints (a,b) and (c,d). The segment is translated so that its image is 6 units up and 3 units left of the preimage. Are the two segments parallel, perpendicular, or neither? Also need a picture of the image and preimage, thanks!

Answer 1

parallel

Explanation:

Translation moves each point the same amount in the same direction. Essentially, the original segment becomes the side of a parallelogram, whose other side is the image, and whose ends are the vectors specifying the translation.

In the attachment, we have designated (a, b) as point A, and (c, d) as point B. We had to choose specific values for these in order to plot them, but the description of the effect of translation applies no matter what the point coordinates are chosen to be.