Question

The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

Which statement correctly describes the relationship between △DEF and △D′E′F′ ?

The triangles are not congruent because △D′E′F′ is a translation of △DEF , and a translation is not a rigid motion.
The triangles are congruent because △D′E′F′ is a rotation of △DEF , and a rotation is a rigid motion.
The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.
The triangles are congruent because △D′E′F′ is a reflection of △DEF , and a reflection is a rigid motion.

Answer 1

Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .

Explanation:

Rigid motions form congruent figures, the common rigid motions are:

1) translation (moves figure about some distance)

2) reflection (creates mirror image)

3) rotation (rotate figure about some degrees)

Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .

Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

Here the coordinates of the image are increased by using a scale factor 2.

So △D′E′F′ must be an enlargement of △DEF.

⇒△D′E′F′ is a dilation of △DEF

It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Answer 2

The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Explanation:

The rule we have is (x, y)→(2x, 2y). This means that each x-coordinate and each y-coordinate are multiplied by 2. This is a dilation by a factor of 2.

This will stretch the image by a factor of 2; this means the sides will be twice as long. This means they will not be congruent.