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Quadrilateral RUST has a vertex at R (1,2). U S What are the coordinates of R'after a dilation by a scale factor of 3, centered at the origin, followed by the translation (x, y) - (x + 2, y)?
A. (5,8)
B. (5,2)
C. (9,6)
D. (5,6)​

Sagot :

xero099

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.

Answer:d

Step-by-step explanation:

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