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.

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

Step-by-step 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.

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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