Question

your turn
the figures shown are congruent. find a sequence of rigid motions that maps one figure to the other. give coordinate notation for the transformations you use. then check your answer.

1. jklm ≅ wxyz

step 1: look at the graph and/or table for similarities and differences.
step 2: look at coordinate - notation rules that could map figure cde onto jkl. (select two)
a rotation
b reflection
c translation
d the figures are not congruent.
step 3: write the coordinate notation for the transformations you use. describe the rule in words. (x,y)→____
step 4: check your answer.
did the two rigid motions map one figure onto to another? why or why not?

Explanation:

Step1: Analyze the orientation and position

By observing the graph, we can see that the two - congruent figures have different orientations and positions. A rotation can change the orientation and a translation can change the position. So we can use a rotation and a translation to map one figure to the other.

Step2: Select the transformation types

We select A. Rotation and C. Translation as the two types of rigid - motions that can map one figure to the other.

Step3: Determine the coordinate notation

First, we can rotate the figure \(WXYZ\) 180° about the origin. The rule for a 180° rotation about the origin is \((x,y)\to(-x, - y)\). Then, we can translate the rotated figure. Let's assume we need to translate it \(a\) units to the right and \(b\) units up. The combined rule is \((x,y)\to(-x + a,-y + b)\). For example, if we first rotate 180° about the origin and then translate 4 units to the right and 4 units up, the rule is \((x,y)\to(-x + 4,-y + 4)\)

Step4: Check the answer

We can take some key points of figure \(WXYZ\), apply the rotation and translation rules, and see if they match the corresponding points of figure \(JKLM\). If the coordinates of all key - points of the transformed figure \(WXYZ\) match the coordinates of the points of figure \(JKLM\), then the two rigid motions map one figure onto the other.

Answer:

Step 2: A. Rotation, C. Translation
Step 3: For example, \((x,y)\to(-x + 4,-y + 4)\) (the values of \(a\) and \(b\) in the translation part may vary depending on the actual situation)