Answer:
see attached
Step-by-step explanation:
You want the given image Q rotated 90° or 180° about various centers.
Rotation
Rotation of an object about a point means the line segment joining the center of rotation to an image point will be the given angle of rotation from the line segment joining the center of rotation to the preimage point. The distance from the center of rotation is unchanged.
Rotation about point (p, q) can be described by the transformations ...
(x, y) ⇒ ((y-q)+p, -(x-p)+q) . . . . . 90° CW
(x, y) ⇒ (-(y-q)+p, (x-p)+q) . . . . . 90° CCW
(x, y) ⇒ (2p-x, 2q-y) . . . . . . . . . . 180° (either direction)
Application
The vertex of the acute angle in the figure is located at (x, y) = (2, -2). We will show the use of these transformations for that point. In general, once you have located one of the vertices of the figure, you can locate the others by considering the direction and distance from each vertex to the next.
a) 90° CW
For center (5, 1), the transformation is ...
(x, y) ⇒ (y+4, 6-x)
(2, -2) ⇒ (-2+4, 6-2) = (2, 4)
The next segment clockwise around the figure will be down 3 units from this point to (2, 1).
b) 90° CCW
For center (-2, -3), the transformation is ...
(x, y) ⇒ (-5-y, x-1)
(2, -2) ⇒ (-5-(-2), 2-1) = (-3, 1)
The next segment clockwise around the figure will be up 3 units from this point to (-3, 4).
c) 180°
For center (1, -4), the transformation is ...
(x, y) ⇒ (2-x, -8 -y)
(2, -2) ⇒ (2 -2, -8 -(-2)) = (0, -6)
The next segment clockwise around the figure will be 3 units left from this point to (-3, -6).
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