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guapka [62]
3 years ago
10

Why do all transformation preserve distance

Mathematics
1 answer:
yuradex [85]3 years ago
7 0
Well, a distance-preserving transformation is called a rigid motion, and the name suggests that it <em>moves the points of the plane around in a rigid fashion.</em>

A transformation is distance-preserving if the distance between the images of any two points and the distance between the two original points are equal.

If that's confusing, I get it; basically if you transform something, the points from the transformation are image points. Take the distance from a pair of image points, and take the distance from a pair of original points, and they should be the same for a <em>rigid </em>motion.

I keep emphasizing this b/c not all transformations preserve distance; a dilation can grow or shrink things. But if you didn't go over dilations, don't say nothin XD
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(8x^3 - x) - (10x - 5x^2 - 3x^3) <br> Show your work.
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Let's simplify step-by-step.
8
x
3
−
x
−
(
10
x
−
5
x
2
−
3
x
3
)
Distribute the Negative Sign:
=
8
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−
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+
−
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(
10
x
−
5
x
2
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−
x
+
−
1
(
10
x
)
+
−
1
(
−
5
x
2
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+
−
1
(
−
3
x
3
)
=
8
x
3
+
−
x
+
−
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x
+
5
x
2
+
3
x
3
Combine Like Terms:
=
8
x
3
+
−
x
+
−
10
x
+
5
x
2
+
3
x
3
=
(
8
x
3
+
3
x
3
)
+
(
5
x
2
)
+
(
−
x
+
−
10
x
)
=
11
x
3
+
5
x
2
+
−
11
x
Answer:
=
11
x
3
+
5
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