Which sequence is not equivalent to the others?
(1) a reflection across the y-axis, followed by a reflection across the x-axis, and then a 90° clockwise rotation about the origin
(2)a 90° clockwise rotation about the origin and then a 180° rotation about the origin
(3) a reflection across the x-axis, followed by a 90° counterclockwise rotation about the origin, and then a reflection across the x-axis
(4) a 90° counterclockwise rotation about the origin

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.

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: