### Video Transcript

When the green triangle is rotated 90 degrees about π΄, which triangle is its new position? (A) Triangle π΄π·πΈ, (B) triangle π΄πΉπΊ, or (C) triangle π΄π»πΌ.

We are asked to rotate triangle π΄π΅πΆ 90 degrees about point π΄. We recall that to rotate a polygon about a point, we first rotate all its vertices. So, weβll need to rotate points π΄, π΅, and πΆ 90 degrees. Since 90 degrees is a positive value, we note that we will rotate all these points counterclockwise.

We recall that we rotate a point π about π΄ by moving it along a circle centered at π΄ with radius π΄π. And the measure of angle ππ΄π prime is equal to the measure of the rotation, where π prime is the image of π. We will follow this procedure to find the image of each vertex of the green triangle.

Letβs start with π΄. π΄ is the center of rotation, so it will not move under this rotation. Next, weβll find the image of vertex π΅. We can draw a ray with endpoint π΄ passing through π΅ and then measure another ray that is 90 degrees in the counterclockwise direction of ray π΄π΅. Letβs name this ray π΄π½. If we then sketch a circle centered at π΄ with radius π΄π΅, we note that π· is the point of intersection between the circle and ray π΄π½ and that the measure of angle π΅π΄π· is 90 degrees. Thus, the image of π΅ after the rotation is π·.

We can follow the same process for vertex πΆ. First, we sketch the ray with endpoint π΄ passing through point πΆ and add another ray that is 90 degrees counterclockwise from ray π΄πΆ. We can then sketch a circle of radius π΄πΆ centered at π΄ and find that the point of intersection between the ray and the circle is point πΈ.

So, the image of π΄ is π΄, the image of π΅ is π·, and the image of πΆ is πΈ. Therefore, the image of triangle π΄π΅πΆ is triangle π΄π·πΈ, which is answer (A).