Answer each of the following:

a. Draw a line l’ and any two points A and B so that AB is
parallel to the line. Find the image of l under a translation
from A to B.
b. Draw a line l and any two points A and B so that AB is
not parallel to l. Construct l’, the image of l under the
translation from A to B.
c. How are l and l’ in part (b) related? Why?

a. To draw a line l' parallel to AB, you can start by drawing a line l and two points A and B on that line. Then, using a ruler, draw a line through A and B. This line will be parallel to line l.

To find the image of line l under a translation from A to B, you can imagine sliding the entire line l along the direction and distance from A to B. The new position of line l after the translation is the image of line l under the translation.

b. To draw a line l and two points A and B where AB is not parallel to l, you can start by drawing a line l. Then, choose two points A and B on that line such that line AB is not parallel to l.

To construct line l', the image of line l under the translation from A to B, you can imagine sliding the entire line l along the direction and distance from A to B. The new position of line l after the translation is the line l'.

c. In part (b), line l and line l' are parallel. This is because when you translate line l from A to B, the two lines remain equidistant at every point. This property of translations is what causes line l' to remain parallel to line l.