Respuesta :

Answer:

Rotation 90 degree counterclockwise then 2 units up.

Step-by-step explanation:

Given : Quadrilateral ABCD and A'B'C'D'.

To find: What transformation were applied to ABCD to obtain A’B’C’D.

Solution: We have given

A (3,6) →→ A'(-6,5)

B( 3,9)→→ B'(-9 ,5)

C(7,9)→→C'(-9 ,9)

D(7,6)→→D'(-6,9)

By the 90 degree rotational rule :   (x ,y) →→(-y ,x) and unit 2 unit up

A (3,6) →→ A'(-6,3) →→ A'(-6,3+2)

B( 3,9)→→ B'(-9 ,3)→→ B'(-9 ,3+2)

C(7,9)→→C'(-9 ,7) →→C'(-9 ,7+2)

D(7,6)→→D'(-6,7)→→D'(-6,7+2)

Therefore, Rotation 90 degree counterclockwise then 2 units up.

The transformation applied is Rotation 90 degree counterclockwise then 2 units up.

What are coordinates?

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

The transformation which was applied to ABCD to obtain A’B’C’D be found by finding the change in the coordinates of the quadrilateral. Therefore,

  • A (3,6)  ⇒  A'(-6,5)
  • B( 3,9)  ⇒  B'(-9 ,5)
  • C(7,9)  ⇒  C'(-9 ,9)
  • D(7,6)  ⇒  D'(-6,9)

As it is observed that the change in the coordinate is 90 degrees counterclockwise then 2 units up. Therefore, the transform of the coordinates can be done as (x ,y)⇒(-y ,x)⇒(-y, x+2).

  • A (3,6) ⇒ A'(-6,3+2)
  • B( 3,9) ⇒ B'(-9 ,3+2)
  • C(7,9) ⇒ C'(-9 ,7+2)
  • D(7,6) ⇒ D'(-6,7+2)

Since the condition holds true, it can be concluded that the transformation applied is Rotation 90 degree counterclockwise then 2 units up.

Learn more about Coordinates:

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