quadrilateral $jklm$ is rotated $-270^\circ$ about the origin.

draw the image of this rotation.

Question

quadrilateral $jklm$ is rotated $-270^\circ$ about the origin.

draw the image of this rotation.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Rotations in the Coordinate Plane", "Geometric Transformations" ], "current_concepts": [ "Rotations in the Coordinate Plane", "Geometric Transformations" ] } ## Identify original coordinates $$ \begin{aligned} J &= (3, 3) \ K &= (5, -5) \ L &= (-3, -7) \ M &= (3, -3) \end{aligned} $$ ## Apply rotation rule $$ \begin{aligned} \text{Rotation of } -270^\circ \text{ (clockwise)} &\equiv \text{Rotation of } 90^\circ \text{ (counterclockwise)} \ (x, y) &\to (-y, x) \end{aligned} $$ ## Calculate image coordinates $$ \begin{aligned} J'(x', y') &= (-3, 3) \ K'(x', y') &= (5, 5) \ L'(x', y') &= (7, -3) \ M'(x', y') &= (3, 3) \end{aligned} $$ The coordinates of the rotated image $J'K'L'M'$ are: $$ \begin{aligned} J' &= (-3, 3) \ K' &= (5, 5) \ L' &= (7, -3) \ M' &= (3, 3) \end{aligned} $$ { "elements": [ { "type": "point", "params": [[3, 3]], "properties": { "name": "J", "color": "#5583F2", "withLabel": true } }, { "type": "point", "params": [[5, -5]], "properties": { "name": "K", "color": "#5583F2", "withLabel": true } }, { "type": "point", "params": [[-3, -7]], "properties": { "name": "L", "color": "#5583F2", "withLabel": true } }, { "type": "point", "params": [[3, -3]], "properties": { "name": "M", "color": "#5583F2", "withLabel": true } }, { "type": "polygon", "params": [[3, 3], [5, -5], [-3, -7], [3, -3]], "properties": { "strokeColor": "#5583F2", "fillColor": "rgba(85, 131, 242, 0.1)", "strokeWidth": 2 } }, { "type": "point", "params": [[-3, 3]], "properties": { "name": "J'", "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[5, 5]], "properties": { "name": "K'", "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[7, -3]], "properties": { "name": "L'", "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[3, 3]], "properties": { "name": "M'", "color": "#F2557F", "withLabel": true } }, { "type": "polygon", "params": [[-3, 3], [5, 5], [7, -3], [3, 3]], "properties": { "strokeColor": "#F2557F", "fillColor": "rgba(242, 85, 127, 0.2)", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Rotations in the Coordinate Plane" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify original coordinates

Apply rotation rule

Calculate image coordinates

Answer: