Question

PLEASE HEKP FAST FAST

1.Find the image of (2, 6) after a counterclockwise rotation of 180° about the origin.

-6,-2

-2,-6

6,-2

2,-6


2.Find the image of (5, 3) after a counterclockwise rotation of 270° about the origin.

3,-5

-3,-5

-5,-3

5,-3


3.Find the image of (2, -3) after a counterclockwise rotation of 90° about the origin.


4.Find the image of (-8, 9) after a counterclockwise rotation of 180° about the origin.


5.The coordinates of the vertices of a triangle are represented by the polygon matrix Which polygon matrix represents the image of the triangle under a 180° counterclockwise rotation about the origin?


6.The coordinates of the vertices of a triangle are represented by the polygon matrix . Which polygon matrix represents the image of the triangle under a 90° counterclockwise rotation about the origin?

Answer 1

1. (-6,-2)

2. (3, -5)

3. (3, 2)

4. (8, -9)

Explanation:

Where's the pic for 5 and 6?

Answer 2

a) (-2,-6)

b) (3, -5)

c) (3 ,2)

d) (8,-9)

Explanation:

a) You have to use the Rotation Matrix, which is
`\left[\begin{array}{ccc}-1&0\\0&-1\\\end{array}\right]` and it has to be multiplied by (x,y) which is equal to (2,6)

Then after the multiplication you´ll obtain (-2,-6)

b) You have to use the Rotation Matrix which is
`\left[\begin{array}{ccc}0&1\\-1&0\\\end{array}\right]` and multiplied for the vector (5,3) you´ll obtain (3, -5)

c) The Rotation Matrix for a rotation of 90° is given by
`\left[\begin{array}{ccc}0&-1\\1&0\\\end{array}\right]` and again after the multiplication you´ll obtain (3,2)

d) The Rotation Matrix is given by
`\left[\begin{array}{ccc}-1&0\\0&-1\\\end{array}\right]` hence after the multiplication fo the roation matrix and the vector you´ll obtain (8,-9)

The answer of 5 and 6 is the matrix that I already wrote down on the excercises.