190,158 views
14 votes
14 votes
For the point A(-3,7) marked on the diagram, find it's image after each of the following:(a) A rotation of 90 degrees counterclockwise about the origin(b) A rotation of 90 degrees clockwise about the origin.

For the point A(-3,7) marked on the diagram, find it's image after each of the following-example-1
User Zoo
by
2.8k points

1 Answer

23 votes
23 votes

Recall that a 90 degree rotation counterclockwise around the origin implies the following transformation of coordinates:

(x, y) --> (-y, x)

Therefore, the rotation in 90 degrees counterclockwise for ( -3, 7) becomes:

(-3, 7) --> (-7, -3)

The going backward with the rotation of 90 degrees around the origing will get us back to the exact orginal point.

Please allow me a little time to make the drawing with the transformed point.

You can see the red point image of point A after the 90 degree rotation. Notice as well the green angle marked with vertex at the origin showing the 90 degree counterclockwise rotation

A rotation 90 degrees clockwise will produce the following result:

(-3, 7) --> (7, 3)

which is shown in the following image

So we see that the transformation is of the form:

(x, y) --> (y, -x)

For the point A(-3,7) marked on the diagram, find it's image after each of the following-example-1
For the point A(-3,7) marked on the diagram, find it's image after each of the following-example-2
User Kushaldsouza
by
2.6k points