Question

complete. 5. give the coordinates of d(-2, -4) after a 270° counterclockwise rotation about the origin. 6. give the coordinates of e(-4, 5) after a 180° counterclockwise rotation about the origin.

Explanation:

Step1: Recall rotation rules

For a 270 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(y, - x)$. For a 180 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-x,-y)$.

Step2: Rotate point D

Given point D$(-2,-4)$, for a 270 - degree counter - clockwise rotation about the origin, using the rule $(y, - x)$, we substitute $x=-2$ and $y = - 4$. So the new coordinates are $(-4,2)$.

Step3: Rotate point E

Given point E$(-4,5)$, for a 180 - degree counter - clockwise rotation about the origin, using the rule $(-x,-y)$, we substitute $x=-4$ and $y = 5$. So the new coordinates are $(4,-5)$.

Answer:

The coordinates of D after a 270 - degree counter - clockwise rotation about the origin are $(-4,2)$. The coordinates of E after a 180 - degree counter - clockwise rotation about the origin are $(4,-5)$.