Question

line segment $xy$ has a length of 5 units. segment $xy$ is rotated $90^{circ}$ clockwise around the origin and then translated 2 units left and 1 unit down to form segment $xy$. what is the length, in units, of line segment $xy$?

Explanation:

Step1: Recall transformation properties

Rotations and translations are rigid - motions. Rigid - motions preserve the shape and size of geometric figures.

Step2: Apply the property to the line segment

Since rotation and translation are rigid - motions, the length of the line segment remains unchanged. Given that the length of segment $XY$ is 5 units, the length of segment $X'Y'$ is also 5 units.

Answer:

5