given the pre-image p(2, -3), determine the image p under each transformation.

reflection over x-axis
choose

reflection over y-axis
choose

rotation 90 degrees around the origin
choose

rotation 180 degrees around the origin
choose

rotation -90 degrees around the origin
choose

Question

given the pre-image p(2, -3), determine the image p under each transformation.

reflection over x-axis
 choose

reflection over y-axis
 choose

rotation 90 degrees around the origin
 choose

rotation 180 degrees around the origin
 choose

rotation -90 degrees around the origin
 choose

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Reflection across Axis" ], "new_concepts": [ "Coordinate Rotations" ], "current_concepts": [ "Reflection across Axis", "Coordinate Rotations" ] } ## Apply reflection rules to $P(2, -3)$ $$ \begin{aligned} &\text{Reflection over } x\text{-axis: } (x, y) \to (x, -y) \implies (2, 3)\ &\text{Reflection over } y\text{-axis: } (x, y) \to (-x, y) \implies (-2, -3) \end{aligned} $$ ## Apply rotation rules to $P(2, -3)$ $$ \begin{aligned} &\text{Rotation } 90^\circ \text{ counterclockwise: } (x, y) \to (-y, x) \implies (3, 2)\ &\text{Rotation } 180^\circ \text{: } (x, y) \to (-x, -y) \implies (-2, 3)\ &\text{Rotation } -90^\circ \text{ (clockwise } 90^\circ\text{): } (x, y) \to (y, -x) \implies (-3, -2) \end{aligned} $$ | No. | Transformation | Image of $P(2, -3)$ | |---|---|---| | 1 | Reflection over $x$-axis | $(2, 3)$ | | 2 | Reflection over $y$-axis | $(-2, -3)$ | | 3 | Rotation $90$ degrees around the origin | $(3, 2)$ | | 4 | Rotation $180$ degrees around the origin | $(-2, 3)$ | | 5 | Rotation $-90$ degrees around the origin | $(-3, -2)$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Rotations" ] }

No.	Transformation	Image of \(P(2, -3)\)
2	Reflection over \(y\)-axis	\((-2, -3)\)
3	Rotation \(90\) degrees around the origin	\((3, 2)\)
4	Rotation \(180\) degrees around the origin	\((-2, 3)\)
5	Rotation \(-90\) degrees around the origin	\((-3, -2)\)

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QUESTION IMAGE

Question

Explanation:

Apply reflection rules to \(P(2, -3)\)

Apply rotation rules to \(P(2, -3)\)

Answer: