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Koordinat titik berikut yang segaris dengan titik P dan Q adalah….

Diketahui koordinat titik straight P left parenthesis 3 comma negative 1 comma 2 right parenthesis space dan space straight Q left parenthesis negative 1 comma 1 comma 0 right parenthesis. Koordinat titik berikut yang segaris dengan titik P dan Q adalah….

A. left parenthesis 9 comma space 4 comma space 5 right parenthesis
B. left parenthesis 9 comma space 2 comma space 5 right parenthesis
C. left parenthesis 9 comma negative 2 comma space 5 right parenthesis
D. left parenthesis 9 comma negative 4 comma space 5 right parenthesis
E. left parenthesis 9 comma negative 4 comma negative 5 right parenthesis

Pembahasan

Diketahui koordinat titik straight P left parenthesis 3 comma negative 1 comma 2 right parenthesis space dan space straight Q left parenthesis negative 1 comma 1 comma 0 right parenthesis, maka

PQ with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 1 row 0 end table close parentheses minus open parentheses table row 3 row cell negative 1 end cell row 2 end table close parentheses equals open parentheses table row cell negative 1 minus 3 end cell row cell 1 plus 1 end cell row cell 0 minus 2 end cell end table close parentheses equals open parentheses table row cell negative 4 end cell row 2 row cell negative 2 end cell end table close parentheses

Misal, titik R merupakan titik yang segaris dengan P dan Q, maka

stack P R with rightwards arrow on top equals k stack P Q with rightwards arrow on top open parentheses table row cell r subscript 1 minus 3 end cell row cell r subscript 2 plus 1 end cell row cell r subscript 3 minus 2 end cell end table close parentheses equals k open parentheses table row cell negative 4 end cell row 2 row cell negative 2 end cell end table close parentheses rightwards arrow r subscript 1 equals negative 4 k plus 3 rightwards arrow r subscript 2 equals 2 k minus 1 rightwards arrow r subscript 3 equals negative 2 k plus 2

untuk k equals negative 3 over 2

r subscript 1 equals negative 4 k plus 3 equals negative 4 open parentheses negative 3 over 2 close parentheses plus 3 equals 9 r subscript 2 equals 2 k minus 1 equals 2 open parentheses negative 3 over 2 close parentheses minus 1 equals negative 4 r subscript 3 equals negative 2 k plus 2 equals negative 2 open parentheses negative 3 over 2 close parentheses plus 2 equals 5

Jadi, jawaban yang tepat adalah D.

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