Question

directions - rotate the point according to each direction; name the new coordinates: starting point (3,5) 90° rotation clockwise 180° rotation clockwise 270° rotation clockwise 360° rotation clockwise

Explanation:

Step1: Recall rotation rules for 90 - degree clockwise

For a 90 - degree clockwise rotation of a point $(x,y)$ about the origin, the new coordinates $(x',y')$ are given by $(y,-x)$. The starting point is $(3,5)$. So, $x = 3$ and $y = 5$. Then $x'=5$ and $y'=- 3$.

Step2: Recall rotation rules for 180 - degree clockwise

For a 180 - degree clockwise rotation of a point $(x,y)$ about the origin, the new coordinates $(x',y')$ are given by $(-x,-y)$. With $x = 3$ and $y = 5$, we have $x'=-3$ and $y'=-5$.

Step3: Recall rotation rules for 270 - degree clockwise

For a 270 - degree clockwise rotation of a point $(x,y)$ about the origin, the new coordinates $(x',y')$ are given by $(-y,x)$. So for $x = 3$ and $y = 5$, we get $x'=-5$ and $y'=3$.

Step4: Recall rotation rules for 360 - degree clockwise

For a 360 - degree clockwise rotation of a point $(x,y)$ about the origin, the new coordinates $(x',y')$ are the same as the original point, i.e., $(x',y')=(x,y)$. So for $x = 3$ and $y = 5$, $x'=3$ and $y'=5$.

Answer:

90° Rotation Clockwise: $(5, - 3)$
180° Rotation Clockwise: $(-3,-5)$
270° Rotation Clockwise: $(-5,3)$
360° Rotation Clockwise: $(3,5)$