Question

original point rotation about the origin 90° clockwise reflection across the x - axis
(9, 5) (5, - 9) (9, - 5)
(-3, 3) (3, 3) (-3, -3)
(-2, -4) (-4, 2) (-2, 4)
(x, y) (y, -x)

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree clockwise rotation about the origin for a point $(x,y)$ is $(y, - x)$.

Step2: Recall reflection rule

The rule for reflecting a point $(x,y)$ across the x - axis is $(x,-y)$.

Step3: Check first row

For the point $(9,5)$, 90 - degree clockwise rotation about the origin gives $(5,-9)$ (using $(y, - x)$ where $x = 9$ and $y = 5$). Reflection across the x - axis of $(5,-9)$ gives $(5,9)$ (using $(x,-y)$ where $x = 5$ and $y=-9$).

Step4: Check second row

For the point $(-3,3)$, 90 - degree clockwise rotation about the origin gives $(3,3)$ (using $(y, - x)$ where $x=-3$ and $y = 3$). Reflection across the x - axis of $(3,3)$ gives $(3,-3)$ (using $(x,-y)$ where $x = 3$ and $y = 3$).

Step5: Check third row

For the point $(-2,-4)$, 90 - degree clockwise rotation about the origin gives $(-4,2)$ (using $(y, - x)$ where $x=-2$ and $y=-4$). Reflection across the x - axis of $(-4,2)$ gives $(-4,-2)$ (using $(x,-y)$ where $x=-4$ and $y = 2$).

Step6: General case

For the point $(x,y)$, 90 - degree clockwise rotation about the origin gives $(y,-x)$. Reflection across the x - axis of $(y,-x)$ gives $(y,x)$.

Answer:

Original Point	Rotation About the Origin 90° Clockwise	Reflection Across the X - AXIS
$(-3,3)$	$(3,3)$	$(3,-3)$
$(-2,-4)$	$(-4,2)$	$(-4,-2)$
$(x,y)$	$(y,-x)$	$(y,x)$