Answer with explanation:
Consider the geometrical shape , which is in the first Quadrant
Option 1:
A reflection across the y-axis, followed by a reflection across the x-axis, and then a 90° clockwise rotation about the origin .
Explanation:
When we reflect the shape across y axis , it will reach in second Quadrant, then by reflection across the x-axis,takes it to the third Quadrant,then a 90° clockwise rotation about the origin takes it to the second Quadrant.
Option 2:
a 90° clockwise rotation about the origin and then a 180° rotation about the origin
Explanation:
90° clockwise rotation about the origin, takes the shape to fourth Quadrant,and then a 180° rotation about the origin takes the shape to Second Quadrant.
Option 3
a reflection across the x-axis, followed by a 90° counterclockwise rotation about the origin, and then a reflection across the x-axis
Explanation:
a reflection across the x-axis, takes the shape in fourth Quadrant,then a 90° counterclockwise rotation about the origin takes the shape in first Quadrant, and again then a reflection across x axis ,takes the shape again in Fourth Quadrant.
Option 4
a 90° counterclockwise rotation about the origin
Explanation:
a 90° counterclockwise rotation about the origin takes the shape in Second Quadrant.
Option 3 That is , Statement 3,⇒ a reflection across the x-axis, followed by a 90° counterclockwise rotation about the origin, and then a reflection across the x-axis, is not equivalent to the other statement.
