A circle centered on the point (-2, 2) with the point A at (1, 2) on its circumference is transformed twice on the coordinate plane. The coordinates of point A and the center of the circle, O, are given in the table as the figure undergoes the transformations. (x, y) (x, y) Point A (1,2) (6,4) (-2,2) (6,1) 1. Determine the transformation that takes point A to point A'. 2. Determine the transformation that takes point A' to point A". O (x", y") (2,1) (2,-2) 3. Write the composition in transformation notation. 4. Write the mapping rule that takes (x, y) to (x y) to (X', y').

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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A circle centered on the point (-2, 2) with the point A at (1, 2) on its circumference is transformed
twice on the coordinate plane. The coordinates of point A and the center of the circle, O, are given
in the table as the figure undergoes the transformations.
Point
(x, y)
(x, y)
A
(1, 2)
(6,4)
(-2,2)
(6, 1)
1. Determine the transformation that takes point A to point A'.
2. Determine the transformation that takes point A' to point A".
O
(x", y")
(2,1)
(2,-2)
3. Write the composition in transformation notation.
4. Write the mapping rule that takes (x, y) to (x y) to (x, y).
Transcribed Image Text:A circle centered on the point (-2, 2) with the point A at (1, 2) on its circumference is transformed twice on the coordinate plane. The coordinates of point A and the center of the circle, O, are given in the table as the figure undergoes the transformations. Point (x, y) (x, y) A (1, 2) (6,4) (-2,2) (6, 1) 1. Determine the transformation that takes point A to point A'. 2. Determine the transformation that takes point A' to point A". O (x", y") (2,1) (2,-2) 3. Write the composition in transformation notation. 4. Write the mapping rule that takes (x, y) to (x y) to (x, y).
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