Question

Quadrilateral RUST has a vertex at R (1, 5).

A. (4,4)
B. (4,8)
C. (3,9)
D. (2,8)

What are the coordinates of R'after the translation (x, y) - (x+1, y-1),
followed by a dilation by a scale factor of 2, centered at the origin?

Answer 1

B. (4, 8)

Explanation:

You want the coordinates of R(1, 5) after translation by (1, -1) and dilation by a factor of 2.

Translation

Applying the given transformation, you have ...

(x, y) ⇒ (x +1, y -1)

R(1, 5) ⇒ R'(1 +1, 5 -1) = R'(2, 4)

Dilation

The dilation multiplies each coordinate value by the dilation factor, 2.

(x, y) ⇒ (2x, 2y)

R'(2, 4) ⇒ R''(2·2, 2·4) = R''(4, 8)

The coordinates after translation and dilation are (4, 8).

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