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Answer:
D. [tex](5,6)[/tex]
Step-by-step explanation:
Let [tex]R(x,y) = (1,2)[/tex], we proceed to perform all operations described on statement:
1) Dilation
[tex]R'(x,y) = O(x,y) + k\cdot [R(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Point of reference.
[tex]R(x,y)[/tex] - Original point.
[tex]R'(x,y)[/tex] - Dilated point.
[tex]k[/tex] - Scale factor.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]R(x,y) = (1,2)[/tex] and [tex]k = 3[/tex], then the dilated point is:
[tex]R'(x,y) = (0,0) +3\cdot [(1,2)-(0,0)][/tex]
[tex]R'(x,y) = (0,0) +3\cdot (1,2)[/tex]
[tex]R'(x,y) = (3,6)[/tex]
2) Translation
[tex]R''(x,y) = R'(x,y) + T(x,y)[/tex] (2)
Where:
[tex]R'(x,y)[/tex] - Original point.
[tex]T(x,y)[/tex] - Translation point.
[tex]R''(x,y)[/tex] - Translated point.
If we know that [tex]R'(x,y) = (3,6)[/tex] and [tex]T(x,y) = (2,0)[/tex], then the translated vector is:
[tex]R''(x,y) = (3,6)+(2,0)[/tex]
[tex]R''(x,y) = (5,6)[/tex]
Therefore, the correct answer is D.