Question

Please help me!!

(30 POINTS!)

1. Consider this sequence of
performed on shape I: dilation by a scale factor of 2. followed by a reflection across the x-ads, and then a translation left 1 unit. Does the sequence prove that shapes I and IV are similar? Explain your answer.

2. Consider this sequence of transformations applied to shape II: a 90 degree clockwise rotation about the origin, followed by a translation 9 units down and 9 units left, then a dilation by a scale factor of 2. Does applying this sequence of transformations to shape II prove that shapes II and III are similar? Explain your answer.

Answer 1

1. To check whether the sequence proves that shape I is similar to shape IV, check whether the given sequence of transformations maps shape I onto shape IV.

1. Dilate shape I by a scale factor of 2.

2. Then, reflect the dilated shape across the x-axis.

3. Finally, translate the reflected shape 1 unit left.

The sequence does map shape I onto shape IV. So, the sequence of transformations proves the two shapes are similar.

2. To check whether the sequence proves that shape II is similar to shape III, check whether the given sequence of transformations maps shape II onto shape III.

1. First, rotate shape II 90° clockwise about the origin.

2. Then, translate the rotated shape 9 units down and 9 units left.

3. Finally, dilate the translated shape by a scale factor of 2.

This sequence doesn’t map shape II onto shape III. So, this sequence doesn’t prove that shapes II and III are similar.

Answer 2

To check whether the sequence proves that shape II is similar to shape III, check whether the given sequence of transformations maps shape II onto shape III.

1. First, rotate shape II 90° clockwise about the origin.

Graph of a quadrilateral in 2nd quadrant and its 90 degree clockwise rotation in 1st quadrant.

2. Then, translate the rotated shape 9 units down and 9 units left.

Graph of a quadrilateral rotated 90 degree clockwise in 1st quadrant and its translation 9 units down and left in 3rd quadrant.

3. Finally, dilate the translated shape by a scale factor of 2.

Graph of a quadrilateral translated 9 units down and left in 3rd quadrant and its dilation by scale factor 2.

This sequence doesn’t map shape II onto shape III. So, this sequence doesn’t prove that shapes II and III are similar.

Explanation: