Question

Please help, i need right answers and be help if it with proof, ty! Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.

Which sequence of transformations will produce the same results?
a reflection over the y-axis and then a rotation 90degree clockwise about the origin
a reflection over the x-axis and then a rotation 90degree clockwise about the origin
a 180degree rotation about the origin
a reflection over the y-axis and then a reflection over the x-axis

Answer 1

A. A reflection over the y-axis and then a rotation 90 degree clockwise about the origin.

Explanation:

Given information: Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.

• This means Figure H is made by G rotated CLOCKWISE and reflected over the X-AXIS.

A sequence of transformations to produce the same results could be the opposite of this, wherein Figure H undergoes a series of transformations to form Figure G.

• A reflection over the y-axis flips figure H like folding a piece of paper in half vertically. To help visualize, the point (5, -2) becomes (-5, -2). A 90 degree clockwise turn about the origin makes the point (-5, -2) on figure H to become (-2, 5). Figure G has the same point at (-2, 5).
• so, a reflection of figure H over the y-axis and then a rotation 90 degree clockwise about the origin will form figure G, thus producing the same results.