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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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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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)  II. (−1, 2)  III. (m, n) interms of m and n  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.  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∘,  Now, rotate the resulting figure to form the image of P(a, b), under 90∘cockwise rotation as under:

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

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