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The horizontal axis ranges from negative 9 to 9. The vertical axis ranges from negative 8 to 10. The vertices of triangle upper L upper O upper W are as follows: upper L at left parenthesis negative 5 comma negative 2 right parenthesis, upper O at left parenthesis negative 2 comma negative 4 right parenthesis, and upper W at left parenthesis negative 4 comma negative 6 right parenthesis. The first horizontal line of reflection is graphed as Y equals 1. The second horizontal line of reflection is graphed as Y equals 7. The vertices of triangle upper L double prime upper O double prime upper W double prime are as follows: upper L double prime at left parenthesis negative 5 comma 10 right parenthesis, upper O double prime at left parenthesis negative 2 comma 8 right parenthesis, and upper W double prime at left parenthesis negative 4 comma 6 right parenthesis. Which of the following transformations maps △LOW to △L''O''W'' ? Select two correct answers.
1) the composite transformation described by ry=1 followed by ry=7
2) the single transformation described by (x, y)→(x, y+12)
3) the single transformation described by (x, y)→(x, y−12)
4) The single transformation described by R270° 5) he composite transformation described by rx=1 followed by rx=7
The horizontal axis ranges from negative 9 to 9. The vertical axis ranges from negative 8 to 10. The vertices of triangle upper L upper O upper W are as follows: upper L at left parenthesis negative 5 comma negative 2 right parenthesis, upper O at left parenthesis negative 2 comma negative 4 right parenthesis, and upper W at left parenthesis negative 4 comma negative 6 right parenthesis. The first horizontal line of reflection is graphed as Y equals 1. The second horizontal line of reflection is graphed as Y equals 7. The vertices of triangle upper L double prime upper O double prime upper W double prime are as follows: upper L double prime at left parenthesis negative 5 comma 10 right parenthesis, upper O double prime at left parenthesis negative 2 comma 8 right parenthesis, and upper W double prime at left parenthesis negative 4 comma 6 right parenthesis. Which of the following transformations maps △LOW to △L''O''W'' ? Select two correct answers.
1) the composite transformation described by ry=1 followed by ry=7
2) the single transformation described by (x, y)→(x, y+12)
3) the single transformation described by (x, y)→(x, y−12)
4) The single transformation described by R270° 5) he composite transformation described by rx=1 followed by rx=7
Answers
GPT-5 mini
Correct answers: 1 and 2.
Reason: Each vertex's y increases by 12 (e.g. -2 → 10), so (x,y) → (x,y+12) (option 2) maps △LOW to △L''O''W''. Reflecting across y=1 then across y=7 is two reflections across parallel lines distance 6 apart, which produces a translation by 2·6 = 12 upward, so option 1 also works.
Reason: Each vertex's y increases by 12 (e.g. -2 → 10), so (x,y) → (x,y+12) (option 2) maps △LOW to △L''O''W''. Reflecting across y=1 then across y=7 is two reflections across parallel lines distance 6 apart, which produces a translation by 2·6 = 12 upward, so option 1 also works.