Question

write the coordiantes of twrite the coordinates of the vertices after a rotation 270 degrees counterclockwise around the origin D( 1,5) D'( )E (1,10) E' ( )F ( 10,10) F' ( ) G ( 10,5) G' ( )

Answer 1

A rotation of 270 degrees counterclockwise is the same as a rotation 90 degrees clockwise.

This rotation will make a point from the first quadrant go to the fourth, from the second to the first, from third to second and from fourth to third.

If the point goes from the first quadrant to the fourth, we change the signal of the x-coordinate.

If the point goes from the second quadrant to the first, we change the signal of the y-coordinate.

If the point goes from the third quadrant to the second, we change the signal of the x-coordinate.

If the point goes from the fourth quadrant to the third, we change the signal of the y-coordinate.

Also, in all those rotations, we need to switch the x and y coordinates between themselves.

So we have that:

`\begin{gathered} D(1,5)\to1st\text{ quadrant}\to D^(\prime)=(1,-5) \\ E(1,10)\to1st\text{ quadrant}\to E^(\prime)=(1,-10) \\ F(10,10)\to1st\text{ quadrant}\to F^(\prime)=(10,-10) \\ G(10,5)\to1st\text{ quadrant}\to G^(\prime)=(10,-5) \end{gathered}`