Answer
Part A
A'' (-4, 8)
B'' (-6, 8)
C'' (-2, 5)
D'' (-8, 5)
Part B
To get polygon ABCD back from polygonA"B"C"D", we
- Rotation by 90 degrees counter clockwise.
- Reflection across the line y = -x
Step-by-step explanation
When a coordinate is reflected about the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed), that is,
A (x, y) becomes A' (-y, -x)
And when the coordinates are further rotated 90 degrees clockwise,
B (x, y) becomes B' (y, -x)
So, we can write the coordinates of the vertices or edges of this polygon and perform the transformations
A (4, 8)
B (6, 8)
C (2, 5)
D (8, 5)
Recall that the reflection about y = -x, changes the coordinates from A (x, y) into A' (-y, -x)
So, the coordinates of this polygon after the reflection, become
A (4, 8) = A' (-8, -4)
B (6, 8) = B' (-8, -6)
C (2, 5) = C' (-5, -2)
D (8, 5) = D' (-5, -8)
Then recall that a rotation of 90 degrees clockwise changes B (x, y) into B' (y, -x).
So, the coordinates change further into
A' (-8, -4) = A'' (-4, 8)
B' (-8, -6) = B'' (-6, 8)
C' (-5, -2) = C'' (-2, 5)
D' (-5, -8) = D'' (-8, 5)
To sketch this on a coordinate system, just mark out the points described by the coordinates and carefully connect.
Part B
We are asked to give a way to take the new polygon A"B"C"D" back to the original polygon ABCD.
This is easy because we just need to reverse the steps we carried out to obtain polygon A"B"C"D"
The original steps were
- Reflection across the line y = -x
- Rotation by 90 degrees clockwise
The reverse operations would be
- Rotation by 90 degrees counter clockwise.
- Reflection across the line y = -x
Hope this Helps!!!