Q:

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.

Accepted Solution

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