Question

You want to transform an object, such that each point (x, y) becomes (2x + 3, 4y + 6). Which of the following sets of transformations should you use?

(A) Scale by (1, 2) then translate by (2, 3)
(B) Scale by (2, 4) then translate by (3, 6)
(C) Translate by (2, 3) then scale by (1, 2)
(D) Translate by (4, 6) then scale by (2, 3)

Answer 1

The correct transformation is option B which describes scaling the object by (2, 4) followed by a translation by (3, 6), directly matching the transformation (2x + 3, 4y + 6).

Step-by-step explanation:

To determine the correct set of transformations that turn each point (x, y) into (2x + 3, 4y + 6), let's analyze the options given.

Option B states that we should first scale the object by (2, 4) and then translate it by (3, 6). Scaling will multiply the x-coordinates by 2 and the y-coordinates by 4, and then translating will add 3 to the x-coordinates and 6 to the y-coordinates. This directly matches the transformation described in the question.

The correct answer is option B: Scale by (2, 4) then translate by (3, 6).