Question

Drag and drop the answers into the boxes to correctly complete the statement.

A sequence of transformations that maps △DEF to △D′E′F′ is a_________ followed by a__________

translation 1 unit left
rotation of 180 about the origin
reflection across the x-axis
rotation of 90 counterclockwise about the origin

Answer 1

A sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 180 about the origin followed by a reflection across the x-axis.

Step-by-step explanation:

A sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 180 about the origin followed by a reflection across the x-axis.

To perform this sequence of transformations, you would first rotate the triangle 180 degrees counterclockwise about the origin. Then, you would reflect the resulting triangle across the x-axis.

These transformations can be visualized as follows:

1. Start with △DEF.
2. Rotate △DEF 180 degrees counterclockwise about the origin to obtain △D′E′F′.
3. Reflect △D′E′F′ across the x-axis to obtain the final transformed triangle.

Answer 2

1. First transformation is rotation rotation of 180 about the origin. This transformation has a rule:

(x,y)→(-x,-y).

If points E(-2,-4), F(-1,-1), D(-2,-1) are vertices of triangle EFD, then

• E(-2,-4)→E''(2,4),
• F(-1,-1)→F''(1,1),
• D(-2,-1)→D''(2,1).

2. Second transformation is translation 1 unit left with a rule

(x,y)→(x-1,y).

Then

• E''(2,4)→E'(1,4),
• F''(1,1)→F'(0,1),
• D''(2,1)→D'(1,1).

Answer: 1st: rotation of 180 about the origin; 2nd: translation 1 unit left.