Przekształcenia geometryczne - odpowiedzi

1. a) tak; b) tak; c) nie; d) tak; e) nie

c) P = (x, y), P' = (-y, 1);

d) P = (x, y), P' =
;

e) P = (x, y), P' = (2x, 3y);

2. a) brak; b) (-1, -1); c) (2; -1,5); d) brak; e) (1, 1);

3. a) a
R; b) a
; c) a
R; d) a
R; e) a=1 lub a= -1.

4. a) A' = (2, -4), B' = (-3, -1), C' = (1, 3), D' = (0, 0), E' = (-5, 2).

b) A' = (-2, 4), B' = (3, 1), C' = (-1, -3), D' = (0, 0), E' = (5, -2).

c) A' = (4, 2), B' = (1, -3), C' = (-3, 1), D' = (0, 0), E' = (-2, -5).

5. a) A' = (-2, -4), B' = (3, -1), C' = (-1, 3), D' = (0, 0), E' = (5, 2).

b) A' = (0, -2), B' = (5, 1), C' = (1, 5), D' = (2, 2), E' = (7, 4).

c) A' = (2, 4), B' = (7, 7), C' = (3, 11), D' = (4, 8), E' = (9, 10).

6. a) y = x - 5, b) y = x + 5, c) y = -x + 5, d) y = -x - 5.

7a. a) y = -3x - 4, b) y =- 3x + 4, c) y = 3x - 4, d) y = 3x + 4.

7b. a) y = 2x - 1 b) y = 2x + 1, c) y = 2x - 3, d) y = 2x.

8. [1, -5]

9. [4, 3]

10. O = (0,5; 3)

11. A' = (-9, -3)

12. A = (5, -5)

13. D = (-4, 8)

14. E = (-2, 4), F = (-1, 0)

15. k = 3 i m = -2

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