Question

problem solving

1. the letter e is shown on the graph grid below. transform the image using the function f shown below.

f(x,y)=(y,x)
did this transformation preserve the size and shape of the image? use tracing paper if necessary.
can you determine which of the four major types of transformations f represents? explain how you determined your answer. use tracing paper to experiment with different transformations.
reasoning

1. transformations that preserve shape and size are called rigid motions. find a definition of just the word rigid using the internet and write it below.

rigid (adj):

1. if a rigid motion was used to transform image a into image b and then a rigid motion was used to transform image b into image c, would image c have to be the same size and shape as image a? explain.

Explanation:

Problem 7

Step1: Understand the transformation

The transformation $F(x,y)=(y,x)$ is a reflection across the line $y = x$. For each point $(x,y)$ on the original letter E, we swap the $x$ and $y$ - coordinates to get the new point.

Step2: Check size and shape preservation

A reflection is a rigid - motion. Rigid motions preserve the size and shape of an image. The distance between any two points in the original figure and the distance between their corresponding points in the transformed figure are equal. So, the size and shape of the letter E are preserved.

Step3: Identify the type of transformation

The four major types of transformations are translation, rotation, reflection, and dilation. Since $F(x,y)=(y,x)$ swaps the $x$ and $y$ - coordinates, it represents a reflection across the line $y = x$. We can verify this using tracing paper by placing it over the original letter E, marking the points, and then flipping the tracing paper across the line $y = x$.

Searching online, the word "rigid" in the context of geometry means not flexible; having a fixed shape and size; unyielding.

Rigid motions preserve shape and size. If Image A is transformed into Image B by a rigid motion, Image B has the same shape and size as Image A. Then, if Image B is transformed into Image C by another rigid motion, Image C has the same shape and size as Image B. By the transitive property, Image C has the same size and shape as Image A.

Answer:

The transformation preserves the size and shape of the image. The transformation $F$ represents a reflection across the line $y = x$.

Problem 8