RIGID MOTION IN A PLANE WORKSHEET

Problem 1 :

Use the graph of the transformation below. 

a. Name and describe the transformation

b. Name the coordinates of the vertices of the image. 

c. Is triangle ABC congruent to image ? 

Problem 2 :

Say, whether the following transformation appear to be isometry. 

Problem 3 :

Do you think that the following transformation appear to be isometry ? Explain your answer. 

Problem 4 :

Is the following transformation appear to be isometry ? 

Problem 5 :

How can we describe the transformation shown below ? 

Problem 6 :

In the diagram shown below, ΔABC is mapped onto ΔXYZ. The mapping is a rotation. Given that ΔABC ---> ΔXYZ is an isometry, find the length of XY and the measure of ∠Z.

Problem 7 :

We are assembling pieces of wood to complete a railing for our porch. The finished railing should resemble the one below. 

Problem 8 :

Many building plans for kayaks show the layout and dimensions for only half of the kayak. A plan of the top view of a kayak is shown below.

a. What type of transformation can a builder use to visualize plans for the entire body of the kayak ?

b. Using the plan above, what is the maximum width of the entire kayak ?

1. Answer :

Part (a) :

The transformation is a reflection in the y-axis. We can imagine that image has been obtained by flipping ΔPQR over the y-axis.

Part (b) :

The coordinates of the vertices of the image, ΔP'Q'R' are P'(4, 1), Q'(3, 5) and R'(1, 1).

Part (c) :

Yes, ΔPQR is congruent to its image ΔP'Q'R'. One way to show this would be to use the Distance Formula to find the lengths of the sides of both triangles. Then use the SSS congruence postulate.

2. Answer :

This transformation appears to be an isometry. The blue parallelogram is reflected in a line to produce a congruent red parallelogram.

3. Answer :

No, this transformation is not an isometry. Because the image is not congruent to the preimage.

4. Answer :

Yes, this transformation appears to be an isometry. The blue quadrilateral is rotated about a point to produce a congruent a congruent red quadrilateral.

5. Answer :

We can describe the transformation shown above by writing,

"ΔPQR is mapped onto ΔSTU"

We can also use arrow notation as follows :

ΔPQR ----> ΔSTU

The order in which the vertices are listed specifies the correspondence. Either of the descriptions implies that

P ----> S

Q ----> T

R ----> U

6. Answer :

The statement "ΔABC is mapped onto ΔXYZ" implies that,

A ----> X

B ----> Y

C ----> Z

Because the transformation is an isometry, the two triangles are congruent.

So, we have

AB = XY = 3 units

∠R = ∠Z = 35°

7. Answer :

Part (a) :

Pieces 1 and 2 are related by a rotation. Pieces 3 and 4 are related by a reflection.

Part (b) :

Knowing how the pieces are related helps us manipulate the pieces to create the desired pattern.

8. Answer :

Part (a) :

The builder can use a reflection to visualize the entire kayak. For instance, when one half of the kayak is reflected in a line through its center, you obtain the other half of the kayak.

Part (b) :

The two halves of the finished kayak are congruent, so the width of the entire kayak will be 2(10), or 20 inches.

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