Which sequence of transformations proves that shape i is similar to shape ii? a. a 90° clockwise rotation about the origin, and then a dilation by a scale factor of 2 b. a reflection across the x-axis, and then a dilation by a scale factor of 1.5 c. a 90° counterclockwise rotation about the origin, and then a dilation by a scale factor of 1.5 d. a reflection across the x-axis, and then a dilation by a scale factor of 2 e. a reflection across the y-axis, and then a dilation by a scale factor of 2

B. a reflection across X axis and then a dilation by a scale factor of 1.5

Step-by-step explanation:

As clear from the graph all the coordinates of image 2 are 1.5 times of image 1 so shape 2 is dilated by the scale factor 1.5.

It is evident from the graph that lines AO and A"O"are parallel to each other so shape 2 is the reflection of shape 1.

Now we calculate the magnitude of line AB

m1 = (y2-y1)/(x2-x1)

    =(-3+6)/(-4.5=9)

    =3/4.5

    =1/1.5

    =2/3

Next we calculate magnitude m2 of A"B"  

m2= (2-4) /(-3+6)

     =(-2/3)

Then we know Tan(180-∅) = -tan∅

similarly if m1=(-m2)

then the one line having magnitude m2 is the rotated image through X axis by 180° of the line having magnitude m1.

So the answer is B.

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