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Use the rule (x, y) → (3x, 2y) to find the image for the preimage defined by thepoints. Determine whether the transformation is a rigid motion. 4. A(3, 5) , B(5, 3) , C(2, 2)How would I be able to work this step by step?

Question

Use the rule (x, y) → (3x, 2y) to find the image for the preimage defined by the
points. Determine whether the transformation is a rigid motion. 
4. A(3, 5) , B(5, 3) , C(2, 2)

How would I be able to work this step by step?

check_circleAnswer
Step 1

Steps to solve this problem

  • 1st find the image of the preimage of the points by the given transformation.
  • Measure the distance between the images.
  • Measure the distance between the preimages.
  • If the distance between the images is equal to the distance between the corresponding preimages, then the transformation is rigid motion otherwise it is not a rigid motion
Step 2

Given,

Each preimage is mapped to its image by the rule or transformation
(x, y)(3x, 2y) and the given points are A (3, 5), B (5, 3), C (2, 2)
So, the image of the given points by the given rule will be
A (3, 5)(3 x 3, 2 x 5) = A'(9,10)
B (5,3)(3 x 5, 2 x 3) B'(15,6)
C (2, 2)(3 x 2,2 x 2) = C'(6,4)
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Image Transcriptionclose

Each preimage is mapped to its image by the rule or transformation (x, y)(3x, 2y) and the given points are A (3, 5), B (5, 3), C (2, 2) So, the image of the given points by the given rule will be A (3, 5)(3 x 3, 2 x 5) = A'(9,10) B (5,3)(3 x 5, 2 x 3) B'(15,6) C (2, 2)(3 x 2,2 x 2) = C'(6,4)

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Step 3

Calculati...

АВ -D (5 — 3)? + (3 — 5)?
= V4 4
BC (2-5)2 (2 3)2
= V9 + 1
V10
A'B' = (15-9)2 (6 10)2
Now
= V36 + 16
= V60
(6 15)2(4 - 6)2
В'С"
V81 + 4
V85
Since, AB A'B' and BC
B'C'
So, we can say that the transformation is not a rigid motion
help_outline

Image Transcriptionclose

АВ -D (5 — 3)? + (3 — 5)? = V4 4 BC (2-5)2 (2 3)2 = V9 + 1 V10 A'B' = (15-9)2 (6 10)2 Now = V36 + 16 = V60 (6 15)2(4 - 6)2 В'С" V81 + 4 V85 Since, AB A'B' and BC B'C' So, we can say that the transformation is not a rigid motion

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