### Video Transcript

If line segment π΄π΅ is rotated about π with a 90-degree angle, which line segment represents its final position? (A) Line segment π·π΄, (B) line segment πΆπ·, or (C) line segment π΅πΆ.

We want to rotate line segment π΄π΅ 90 degrees about point π. We recall that rotating by a positive value is rotating in the counterclockwise direction. To rotate a line segment, we recall that we can just rotate the endpoints. In other words, the image of line segment π΄π΅ would be line segment π΄ prime π΅ prime.

Letβs start by finding the image of π΄. We want to rotate point π΄ 90 degrees about point π by finding point π΄ prime, which is counterclockwise on the circle shown here centered at π of radius π΄π such that the measure of angle π΄ππ΄ prime is equal to 90 degrees.

We can do this by noticing that the distance between π and any vertex of the square is the same. So, all the vertices lie on the circle of radius π΄π centered at π. Then, we can measure the angles at the center of the square by noting that these angles are congruent and their measures sum to 360 degrees. So, each of the four angles at the center measure 90 degrees. Thus, the measure of angle π΄ππ΅ is equal to 90 degrees. And we see that π΄ prime is equal to π΅. Then, we can follow the same reasoning to show that π΅ prime is equal to πΆ.

Hence, the image of line segment π΄π΅ after a rotation of 90 degrees is line segment π΅πΆ, which is answer (C).