The coordinates of the vertices of △DEF△DEF are D(2,−1)D(2,−1) , E(7,−1)E(7,−1) , and F(2,−3)F(2,−3) .

The coordinates of the vertices of △D′E′F′△D′E′F′ are D′(0,−1)D′(0,−1) , E′(−5,−1)E′(−5,−1) , and F′(0,−3)F′(0,−3) .

What is the sequence of transformations that maps △DEF△DEF to △D′E′F′△D′E′F′ ?

Below are the choices that can be found elsewhere:

translation 2 units right
rotation of 180 degrees around the origin
reflection across the y-axis
translation 2 units up

I think the answer is translation 2 units right. I hope it helps.

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ColinJacobus ColinJacobus · Answer 2 · 2019-10-01T16:01:43+02:00

Answer: The required transformation is (x, y) ⇒ (x-2, y).

Step-by-step explanation: Given that the co-ordinates of the vertices of △DEF△DEF are D(2,−1), E(7,−1), and F(2,−3). and the coordinates of the vertices of △D′E′F′ are D′(0,−1), E′(5,−1) and F′(0,−3).

We are to find the sequence of transformations that maps △DEF to △D′E′F′.

We note the following translation holds between the vertices of △DEF to △D′E′F′ :

D(2, -1) ⇒ D'(2-2, -1) = D'(0, -1),

E(7, -1) ⇒ E'(7-2, -1) = E'(5, -1),

F(2, -3) ⇒ F'(2-2, -3) = F'(0, -3).

Therefore, the sequence of transformation is the translation of 2 units towards left.

That is, if (x, y) is a vertex of △DEF, then the corresponding vertex of △D′E′F′, is given by

(x, y) ⇒ (x-2, y).

Thus, the required transformation is (x, y) ⇒ (x-2, y).