Question

point (2,3) is rotated 90 degrees clockwise. what are the new coordinates? (5,6) (3,-2) (3,4) (6,7) point (6,7) is rotated 270 degrees counter clockwise. what are the new coordinates? (7,-6) (7,8) (9,0) (4,5)

Explanation:

Step1: Recall 90 - degree clockwise rotation rule

For a 90 - degree clockwise rotation of a point $(x,y)$ about the origin, the new coordinates $(x',y')$ are given by $(y, - x)$. Given the point $(2,3)$, we substitute $x = 2$ and $y = 3$ into the rule.
$x'=3$, $y'=- 2$
So the new coordinates of the point $(2,3)$ after a 90 - degree clockwise rotation are $(3,-2)$.

Step2: Recall 270 - degree counter - clockwise rotation rule

A 270 - degree counter - clockwise rotation is the same as a 90 - degree clockwise rotation. For a point $(x,y)$ rotated 270 degrees counter - clockwise about the origin, using the rule $(y, - x)$. Given the point $(6,7)$, we substitute $x = 6$ and $y = 7$ into the rule.
$x'=7$, $y'=-6$
So the new coordinates of the point $(6,7)$ after a 270 - degree counter - clockwise rotation are $(7,-6)$.

Answer:

1. B. $(3,-2)$
2. A. $(7,-6)$