Transformations Project Problems

<p> Plot the new coordinates of Triangle `ABC` after a translation `1` unit to the right and `5` units down to become Triangle `EFG`.</p><selectivedisplay><LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 15, "x_interval": 1, "y_interval": 1, "show_grid_section": true, "show_x_axis": true, "show_y_axis": true, "show_x_axis_label": true, "show_y_axis_label": true, "show_x_axis_points": true, "show_y_axis_points": true }, "points": [ { "id": 2, "x": 1, "y": 2, "show_point": true, "label": "A", "label_position": "above", "highlight_point": false, "highlight_point_color": "black", "x_coordinate_highlight": true, "y_coordinate_highlight": true }, { "id": 3, "x": -8, "y": 2, "show_point": true, "label": "B", "label_position": "left", "highlight_point": false, "highlight_point_color": "black", "x_coordinate_highlight": true, "y_coordinate_highlight": true }, { "id": 4, "x": 8, "y": -1, "show_point": true, "label": "C", "label_position": "below", "highlight_point": false, "highlight_point_color": "black", "x_coordinate_highlight": true, "y_coordinate_highlight": true } ], "line_segments": null, "transformation": { "type": "", "deg": 180, "original_polygon_color": "#080808", "show_indicator": "false", "transformed_polygon_color": "#FFA500", "show_polygon_number": false }, "alternative_transformation": null }'></LineGraph ></selectivedisplay>

<p>Figure `ABC` is reflected over the `y`-axis to create Figure `PQR`.</p><p>Draw Figure `PQR`.</p><selectivedisplay data-props='{"show_in_create":true, "show_in_problem_qa": true}'><InteractiveGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 15, "x_interval": 1, "y_interval": 1 }, "points": [ { "id": 0, "is_interactive": false, "label": "A", "x": -6, "y": -3, "label_color": "black", "color": "black" }, { "id": 1, "is_interactive": false, "label": "B", "x": -2, "y": 0, "label_color": "black", "color": "black" }, { "id": 2, "is_interactive": false, "label": "C", "x": -6, "y": -9, "label_color": "black", "color": "black" }, { "id": 3, "is_interactive": true, "label": "P", "label_color": "black", "color": "blue" }, { "id": 4, "is_interactive": true, "label": "Q", "label_color": "black", "color": "blue" }, { "id": 5, "is_interactive": true, "label": "R", "label_color": "black", "color": "blue" } ], "line_segments": [ { "first_point_id": 0, "second_point_id": 1, "color": "black", "is_segment": true }, { "first_point_id": 1, "second_point_id": 2, "color": "black", "is_segment": true }, { "first_point_id": 2, "second_point_id": 0, "color": "black", "is_segment": true }, { "first_point_id": 3, "second_point_id": 4, "color": "blue", "is_segment": true }, { "first_point_id": 4, "second_point_id": 5, "color": "blue", "is_segment": true }, { "first_point_id": 5, "second_point_id": 3, "color": "blue", "is_segment": true } ], "polygons": [ { "id": 0, "num_of_points": 3, "polygon_points_id": [ 0, 1, 2 ], "polygon_fill_color": "#BEBEC033", "is_interactive": false }, { "id": 1, "num_of_points": 3, "polygon_points_id": [ 3, 4, 5 ], "polygon_fill_color": "#0066FF33" } ], "total_interactive_inputs": 3, "mode": "POLYGON"}'></InteractiveGraph ></selectivedisplay>

<p>What are the direction and angle of rotation from Figure `ABC` to Figure `PQR`?</p><LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 15, "x_interval": 1, "y_interval": 1, "x_skip_interval":5,"y_skip_interval":5, "show_grid_section": true, "show_x_axis": true, "show_y_axis": true, "show_x_axis_label": true, "show_y_axis_label": true, "show_x_axis_points": true, "show_y_axis_points": true, "title": "" }, "points": [ { "id": 1, "x": -4, "y": -3, "show_point": true, "highlight_point": false, "highlight_point_color": "red", "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "label": "A", "label_position": "above" }, { "id": 2, "x": 0, "y": -5, "show_point": true, "highlight_point": false, "highlight_point_color": "red", "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "label": "B", "label_position": "right" }, { "id": 3, "x": -7, "y": -7, "show_point": true, "highlight_point": false, "highlight_point_color": "red", "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "label": "C", "label_position": "left" } ], "line_segments": null, "transformation": { "type": "ROTATE", "deg": 180, "show_indicator": false, "show_polygon_number": false, "transformed_polygon_color": "#377CF6", "points": [ { "label": "P", "label_position": "below", "show_point": true, "highlight_point": false, "highlight_point_color": "#377CF6" }, { "label": "Q", "label_position": "left" , "show_point": true, "highlight_point": false, "highlight_point_color": "#377CF6" }, { "label": "R", "label_position": "right" , "show_point": true, "highlight_point": false, "highlight_point_color": "#377CF6" } ], "original_polygon_color": "red" }}'></LineGraph >

<p>Dilate Triangle `ABC` with a scale factor of `2.5` to create Triangle `DEF`.</p><p>Use the origin as the center of dilation.</p><selectivedisplay data-props='{"show_in_create":true,"show_in_problem_qa": true}'> <LineGraph data-props='{ "options": { "x_min": -10, "y_min": -10, "y_max": 10, "x_max": 10, "cell_size": 20, "x_interval": 1, "y_interval": 1 }, "points": [ { "id": 1, "x": -4, "y": 0, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "label": "A" }, { "id": 2, "x": -2, "y": 2, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "label": "B" }, { "id": 3, "x": 4, "y": 0, "show_point": true, "highlight_point": true, "highlight_point_color": "black", "x_coordinate_highlight": true, "y_coordinate_highlight": true, "show_x_intercept_point": false, "show_y_intercept_point": false, "show_coordinates": false, "show_x_intercept": false, "show_y_intercept": false, "label": "C" } ], "line_segments": [ { "first_point_id": 1, "second_point_id": 2, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 2, "second_point_id": 3, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" }, { "first_point_id": 3, "second_point_id": 1, "show_start_arrow": false, "show_end_arrow": false, "highlight_line": "black" } ]}'></LineGraph ></selectivedisplay>