Answer:
- First choice: 90° clockwise rotation around the origin, then a reflection across the x-axis.
Explanation:
The vertices of the figure 1 are:
- (-3, 2)
- (-4, 5)
- (-3, 8)
- (-7,5)
The vertices of figure 2 are:
- (2, -3)
- (5, -4)
- (8, -3)
- (5, -7)
By simple inspection, you can tell that if you rotate the figure 1 90º clockwise and then reflect the image across the x-axys you obtain the figure 2.
You can prove that analitically.
1. Rotation 90º clockwise
A 90º clockwise reotation is the same that a 270º counterclockwise rotation and the mathematical rule for this is:
Applying that rule to the vertices of figure 1, you obtain:
- (-3, 2) → (2, 3)
- (-4, 5) → (5, 4)
- (-3, 8) → (8, 3)
- (-7,5) → (5, 7)
2. Reflection across the x-axis.
A reflection across the x-axis keeps the same x-coordinate and changes the sign of the y-coordinate. The rule is:
Applying that rule to the previous points yields to:
- (2, 3) → (2, -3)
- (5, 4) → (5, -4)
- (8, 3) → (8, -3)
- (5, 7) → (5, -7)
Which are the coordinates of the figure 2. Thus, you have proved that the sequence of transformations 90° clockwise rotation around the origin, then a reflection across the x-axis (first choice) maps the figure 1 to figure 2.
