Question

square m and square p are similar. which sequence of transformations could be applied to square m to map it to square p? a a reflection over the x - axis followed by a translation up b a reflection over the y - axis followed by a translation to the right c a reflection over the x - axis followed by a dilation by a factor less than 1 d a reflection over the y - axis followed by a dilation by a factor greater than 1

Explanation:

Step1: Analyze the orientation and size

• Square \(M\) and \(P\) are not in the same orientation (so a reflection is needed).
• Square \(P\) is larger than square \(M\) (so a dilation with a factor greater than \(1\) is needed).
• A reflection over the \(x -\)axis changes the orientation of the square vertically.
• A dilation by a factor greater than \(1\) will increase the size of the square.

Step2: Check each option

• Option A: A reflection over the \(x -\)axis followed by a translation up will not change the size of the square.
• Option B: A reflection over the \(y -\)axis followed by a translation to the right will not change the size of the square.
• Option C: A reflection over the \(x -\)axis followed by a dilation by a factor less than \(1\) will make the square smaller.
• Option D: A reflection over the \(y -\)axis followed by a dilation by a factor greater than \(1\) changes the orientation (reflection) and increases the size (dilation with factor \(> 1\)).

Answer:

D. a reflection over the y - axis followed by a dilation by a factor greater than 1