What is the image point of the point (4,0) after rotation of 270 degree counterclockwise about the origin

3 answers
Question:

What is the image point of the point (4,0) after rotation of 270 degree counterclockwise about the origin

Answers

C) [tex]W'(1, 3), X'(4, 2), Y'(1, -3), Z'(-3, 0)[/tex]

Step-by-step explanation:

Given co-ordinates are

[tex]W(-3,1)[/tex][tex]X(-2,4)[/tex][tex]Y(-3,1)[/tex][tex]Z(0,3)[/tex]

When we rotate 90° the x-coordinate of [tex]W[/tex] became the y-coordinate of [tex]W'[/tex]. Also y-coordinate of [tex]W'[/tex] is opposite of x-coordinate of [tex]W[/tex].

We have [tex]W=(-3,1)[/tex]

So, [tex]W'=(1,3)[/tex]

Similarly

[tex]X'=(4, 2)\\Y'=(1, -3)\\Z'=(-3, 0)[/tex]

The coordinates of the vertices of each image are:

W' = (1 , 3) , X' = (4 , 2) , Y' = (1 , -3) , Z' = (-3 , 0) ⇒ C

Step-by-step explanation:

Let us revise the rotation about the origin

If point (x , y) rotated about the origin by angle 90° counterclockwise, then its image is (-y , x)If point (x , y) rotated about the origin by angle 180° counterclockwise, then its image is (-x , -y)If point (x , y) rotated about the origin by angle 270° counterclockwise, then its image is (y , -x)If point (x , y) rotated about the origin by angle 90° clockwise, then its image is (y , -x)If point (x , y) rotated about the origin by angle 180° clockwise, then its image is (-x , -y)If point (x , y) rotated about the origin by angle 270° clockwise, then its image is (-y , x)There is no difference between rotating 180° clockwise or  counterclockwise around the origin

∵ The vertices of the figure are W (-3 , 1) , X (-2 , 4) , Y (3 , 1) , Z (0 , -3)

∵ The figure is rotated 90° clockwise (270° counterclockwise)

    about the origin

- Change the sign of the x-coordinate of each point and switch the

  two coordinates as the 3rd or 4th rule above

∴ W' = (1 , 3) , X' = (4 , 2) , Y' = (1 , -3) , Z' = (-3 , 0)

The coordinates of the vertices of each image are:

W' = (1 , 3) , X' = (4 , 2) , Y' = (1 , -3) , Z' = (-3 , 0)

Learn more:

You can learn more about rotation in

#LearnwithBrainly

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