a) To find: The images of the following points under under a 90^circ rotation counterclockwise about the origin: I. (2, 3) II. (-1, 2) III, (m,n) inte

Tammy Todd 2020-12-01 Answered

a) To find:
The images of the following points under under a 90 rotation counterclockwise about the origin:
I. (2, 3)
II. (1, 2)
III, (m,n) interms of m and n
b)To show:
That under a half-turn with the origin as center, the image of a point (a, b) has coordinates (a, b).
c) To find:
The image of P(a, b)under the rotation clockwise by90 about the origin.

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Expert Answer

dessinemoie
Answered 2020-12-02 Author has 90 answers

a) Given:
The image will have a 90 rotation counterclockwise a about the origin.
Approach:
A rotation is a transformation of the plane determined by holding one point the center fixed and rotating the plane about this point by a certain angle clockwise (negative) or counterclockwise (positive).
Calculation:
I. (2, 3)
image
II. (1, 2)
image
III. (m, n) interms of m and n
image
b) Given:
Under a half-turn with the origin as center the image of a point (a, b) has coordinates (a, b).
Approach:
A rotation is a transformation of the plane determined by holding one point-the center-fixed and rotating the plane about this point by a certain angle clockwise (negative) or counterclockwise (positive).
Calculation:
While taking half-turn rotation with center at the origin for (x, y) the image of it will fall into xy-plane with coordinates (x, y), thus the coordinates of the image of a point (a, b) will be (a, b) as shown in the graph below.
image
c) Given:
A point P(a, b).
Approach:
A rotation is a transformation of the plane determined by holding one point-the center-fixed and rotating the plane about this point by a certain angle clockwise (negative) or counterclockwise (positive).
Calculation:
The rotation of 180 about a point is a half-turn is a rotation thus it has all the properties of rotations.
The image of P(b, a) counterclockwise while turn of 180 will give the desired image as P(b, a), i.e., clockwise.
The graphical representation is as under:
As given in question to take the reference from point (a) for turn of 90,
image
Now, rotate the resulting figure to form the image of P(a, b), under 90cockwise rotation as under:
image

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