Question

Figure FGH has vertices located at F(1, 3), G(–1, 2), and H(2, 1). The figure is rotated using the origin as the center of rotation. The image has vertices located at F’(3, –1), G’(2, 1), and H’(1, –2). Which rotation could have taken place?

a 45° clockwise rotation
a 90° clockwise rotation
a 90° counterclockwise rotation
a 180° counterclockwise rotation

Answer 1

Answer: The correct option is

(B) a 90° clockwise rotation.

Step-by-step explanation: Given that the co-ordinates of the vertices of figure FGH are F(1, 3), G(–1, 2) and H(2, 1).

The figure FGH is rotated using origin as the center of rotation and the the co-ordinates of the vertices of image figure F'G'H' are F'(3, -1), G'(2, 1) and H'(1, -2).

We are to select the type of rotation that could have taken place.

The transformation from the vertices of FGH to the vertices of image F'G'H' is

F(1, 3) ⇒ F'(3, -1),

G(-1, 2) ⇒ G'(2, 1),

H(2, 1) ⇒ H'(-1, 2).

Therefore, the transformation rule is (x, y) ⇒ (y, -x). This gives the rotation about origin through an angle of 90°.

Thus, the rotation of 90° clockwise taken place from figure FGH to image F'G'H'.

Option (B) is correct.

Answer 2

using a graph tool
see the attached figure

the answer is the option
a 90° clockwise rotation