Question

Triangles def and d′e′f′ are shown on the coordinate plane below: triangle def and triangle d prime e prime f prime with ordered pairs at d negative 1, 6, at e 1, 3, at f 6, 3, at d prime 6, 1, at e prime 3, negative 1, at f prime 3, negative 6. What rotation was applied to triangle def to create triangle d′e′f′?

1) None of the above
2) 90° counterclockwise
3) 180°
4) 90° clockwise

Answer 1

Upon comparing the coordinates of the vertices of triangle DEF with those of triangle D' E' F', it's evident that the required transformation is a 90° clockwise rotation around the origin.

Step-by-step explanation:

To determine which rotation was applied to triangle DEF to create triangle D' E' F', we need to analyze the coordinates of the vertices before and after the transformation. The original triangle DEF has vertices at D(-1, 6), E(1, 3), and F(6, 3). After the transformation, the vertices of triangle D' E' F' are at D'(6, 1), E'(3, -1), and F'(3, -6).

A 90° clockwise rotation about the origin (0,0) would move a point (x, y) to a new position (y, -x). Comparing the points, we see that D(-1, 6) becomes D'(6, 1), E(1, 3) becomes E'(3, -1), and F(6, 3) becomes F'(3, -6), which all match the 90° clockwise rotation rule. Therefore, triangle DEF was rotated 90° clockwise to obtain triangle D' E' F'.