Which of the following compositions produces the same image as ro,-180°? a. ro,90°o ro,-90° b. ro,-90° o t 2,0 c. rx ° t 1.1 d. ry ° rx

Option: D is the correct answer.

D. ry ° rx

( which is a composition of a reflection along the x-axis and then along the y-axis)

Step-by-step explanation:

We know that if some point is in first quadrant and it is rotated clockwise about the origin by an angle 180 degree then the transformed point will be obtained in the third quadrant.

i.e. the two points lie in a straight line.

Let us consider a point (1,2) and see which matches the below transformation.

Ro,-180°(1,2)=(-1,-2)   ( i.e. it is a rotation of a point or a figure 180 degree about origin)

i.e. (1,2) → (-1,-2)

A)

Ro,90°o Ro,-90°  ( It is a composition of a rotation of a point 90 degree first in the clockwise and then in the anticlockwise direction)

Rotation of a figure 90 degree clockwise holds the rule:

 (x,y) → (-y,x)

Rotation of a figure 90 degree anticlockwise holds the rule:

 (x,y) → (-y,x)

Ro,90°o Ro,-90°(1,2)=Ro,90°(2,-1)

                                = (1,2)

i.e. (1,2) → (1,2)

B)

Ro,-90° o T 2,0 ( which is a composition of translation of a point and then a rotation clockwise 90 degree )

The rule of translation is:

(x,y) → (x+2,y+0)

Ro,-90° o T 2,0 (1,2)=Ro,-90° (3,2)

                               =  (2,-3)

Hence,  (1,2) → (2,-3)

C)

rx ° T 1.1 ( it is a composition of a translation of a point and reflection about x-axis )

The rule of translation is:

(x,y) → (x+1,y+1)

the rule of reflection about x-axis is:

(x,y) → (x,-y)

rx ° T 1.1 (1,2)= rx (2,3)

                   =   (2,-3)

Hence,  (1,2) → (2,-3)

D)

ry ° rx  ( it is a composition of reflection about x-axis and about y-axis respectively)

The rule of reflection about y-axis is:

(x,y) → (-x,y)

ry ° rx (1,2)= ry (1,-2)

                = (-1,-2)

Hence, (1,2) → (-1,-2)

Hence, option: D is the correct answer.

step-by-step explanation:

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step-by-step explanation: