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Giải bài 5 trang 45 SGK Toán 10 tập 2 – Chân trời sáng tạo

Tìm tọa độ a) Điểm H là hình chiếu vuông góc của M trên trục Ox b) Điểm M’ đối xứng với M qua trục Ox c) Điểm K là hình chiếu vuông góc của M trên trục Oy d) Điểm M’’ đối xứng với M qua trục Oy e) Điểm C đối xứng với M qua gốc tọa độ

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Đề bài

Cho điểm \(M\left( {{x_0};{y_0}} \right)\). Tìm tọa độ a) Điểm H là hình chiếu vuông góc của M trên trục Ox b) Điểm M’ đối xứng với M qua  trục Ox c) Điểm K là hình chiếu vuông góc của M trên trục Oy d) Điểm M’’ đối xứng với M qua  trục Oy e) Điểm C  đối xứng với M qua  gốc tọa độ

Lời giải chi tiết

 

a) H là hình chiếu vuông góc của M trên trục Ox nên tọa độ điểm H là \(H\left( {{x_0};0} \right)\)b) M’ đối xứng với M qua  trục Ox nên H là trung điểm của MM’Suy ra \({x_{M'}} = 2{x_H} - {x_M} = 2{x_0} - {x_0} = {x_0};{y_{M'}} = 2{y_H} - {y_M} = 2.0 - {y_0} =  - {y_0}\)Vậy tọa độ điểm M’  là \(\left( {{x_0}; - {y_0}} \right)\)c) K là hình chiếu vuông góc của M trên trục Oy  nên tọa độ điểm K  là \(K\left( {0;{y_0}} \right)\)d) M’’ đối xứng với M qua  trục Oy nên K là trung điểm của MM’’Suy ra \({x_{M''}} = 2{x_K} - {x_M} = 2.0 - {x_0} =  - {x_0};{y_{M''}} = 2{y_K} - {y_M} = 2{y_0} - {y_0} = {y_0}\)Vậy tọa độ điểm M''  là \(\left( { - {x_0};{y_0}} \right)\)e) C đối xứng với M qua  gốc tọa độ nên O là trung điểm của MCSuy ra \({x_C} = 2{x_O} - {x_M} = 2.0 - {x_0} =  - {x_0};{y_C} = 2{y_O} - {y_M} = 2.0 - {y_0} =  - {y_0}\)Vậy tọa độ điểm C  là \(\left( { - {x_0}; - {y_0}} \right)\)

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