Given the vertices of δabc are a (2, -5,) b (-4, 6) and c (3, 1), find the vertices following each of the transformations from the original vertices :
(i honestly have no idea what to do and i really need with this one)

I. A' =  (5,-5), B' = (-1,6), C' = (6,1)

II. A' =  (5,-11), B' = (-1,0), C' = (6,-5)

III. A' = (-5,-2), B = (6,4), C' = (1,-3)

Step-by-step explanation:

We are given the vertices of ΔABC as A = (2,-5), B = (-4,6) and C = (3,1).

I. It is required to 'reflect the triangle about the line x= 3'.

This rule changes (x,y) to (x+3,y).

So, the new vertices are given by,

A' = (2+3,-5) = (5,-5)

B' = (-4+3,6) = (-1,6)

C' = (3+3,1) = (6,1)

II. It is required to 'translate the triangle 3 units to the right and 6 units down'.

This rule changes (x,y) to (x+3,y-6).

So, the new vertices are given by,

A' = (2+3,-5-6) = (5,-11)

B' = (-4+3,6-6) = (-1,0)

C' = (3+3,1-6) = (6,-5)

III. It is required to 'rotate the triangle by 90° about the origin counter-clockwise'.

This rule changes (x,y) to (y,-x).

So, the new vertices are given by,

A = (2,-5) implies A' = (-5,-2)

B = (-4,6) implies B = (6,4)

C = (3,1) implies C' = (1,-3)

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068