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)

28

step-by-step explanation:

8+8+6+6