The shaded octagon is transformed to the unshaded octagon in the coordinate plane below. which statement about the transformation is true? a. the unshaded octagon is a reflection because it is a flip over a diagonal line. b. the unshaded octagon is a dilation because it is smaller than the shaded octagon. c. the unshaded octagon is a horizontal translation because it is directly to the left of the shaded octagon. d. the unshaded octagon is a vertical translation because it is directly under the shaded octagon.

The un-shaded octagon is a reflection because it is a flip over a diagonal line (y = -x) ⇒ answer A

Step-by-step explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

- If the point (x , y) translated horizontally to the right by h units

 ∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 ∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

 ∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

 ∴ Its image is (x , y - k)

* Lets solve the problem

- Look to the answer

# Answer D is wrong because the un-shaded octagon is not a vertical

  translation because it is not directly under the shaded octagon.

# Answer C is wrong because the un-shaded octagon is not a

  horizontal translation because it is not directly to the left of

  the shaded octagon

# Answer B is wrong because the un-shaded octagon is not a dilation

  because it is not smaller or bigger than the shaded octagon it has

  the same size

# The answer A is the right because:

∵ The shaded octagon in the first quadrant and the un-shaded

   octagon in the third quadrant

∵ The vertex of (2 , 1.5) has image (-1.5 , -2)

- The coordinates are replaced by each other the their signs are

 changed

∴ The shaded is reflected across the line y = -x

* The un-shaded octagon is a reflection because it is a flip over a

  diagonal line (y = -x)

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.