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