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3 years ago

1. Which of these transformations are isometries? The diagrams are not drawn to scale.

Mathematics

1 answer:

lisov135 [29]3 years ago

6 0

In math, an isometry is a congruent transformation in which the distance (or length) and the angle is preserved or remains the same even after the transformation.

The transformation can be translation, rotation, reflection, etc.

Let us not use this definition of isometry to answer our question, one at a time.

(I) In here, as we can see the distances 10 and 5 and the angle 43 degrees has been preserved. So, <u>this is an isometry.</u>

(II) In here, distances have been halved, so this is<u> not an isometry</u>, even though the angles have been preserved.

(III) In here, the corresponding distances and the angles have been preserved. So, <u>this is an isometry.</u>

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<h3>Answer: Reflect over the y axis</h3>

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Explanation:

We have these two given functions

f(x) = x+7
g(x) = -x+7

The change is that the x has been replaced with -x

We can say

f(x) = x+7

f(-x) = -x+7 ... replace each x with -x

g(x) = f(-x)

g(x) = -x+7

When we replace x with -x, we're flipping the x inputs from positive to negative, and vice versa. This visually will reflect the line over the vertical y axis. A point like (1,8) on f(x) reflects over to (-1,8) on g(x).

As another example, the point (-5,2) on f(x) reflects over the y axis to arrive at (5,2) on the g(x) function.

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Step-by-step explanation:

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