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3 years ago

How are rigid transformations and congruent figures related

1 answer:

3 0

Hello there.

How are rigid transformations and congruent figures related
<span>Both you can Turn, Flip and or Slide one so it fits exactly on the other.</span>

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What is the midpoint of 0.01 and 0.02

Sliva [168]

Hi! 0.015 is between 0.01 and and 0.02. Your welcome.

7 0

3 years ago

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26. Define a relation ∼ ∼ on R 2 R2 by stating that ( a , b ) ∼ ( c , d ) (a,b)∼(c,d) if and only if a 2 + b 2 ≤ c 2 + d 2 . a2+

Tresset [83]

Answer:

~ is reflexive.

~ is asymmetric.

~ is transitive.

Step-by-step explanation:

~ is reflexive:

i.e., to prove $\forall (a, b) \in \mathbb{R}^2$ , $(a, b) R(a, b)$ .

That is, every element in the domain is related to itself.

The given relation is $\sim: (a,b) \sim (c, d) \iff a^2 + b^2 \leq c^2 + d^2$

Reflexive:

$(a, b) \sim (a, b)$ since $a^2 + b^2 = a^2 + b^2$

This is true for any pair of numbers in $\mathbb{R}^2$ . So, $\sim$ is reflexive.

Symmetry:

$\sim$ is symmetry iff whenever $(a, b) \sim (c, d)$ then $(c, d) \sim (a, b)$ .

Consider the following counter - example.

Let (a, b) = (2, 3) and (c, d) = (6, 3)

$a^2 + b^2 = 2^2 + 3^2 = 4 + 9 = 13$

$c^2 + d^2 = 6^2 + 3^2 = 36 + 9 = 42$

Hence, $(a, b) \sim (c, d)$ since $a^2 + b^2 \leq c^2 + d^2$

Note that $c^2 + d^2 \nleq a^2 + b^2$

Hence, the given relation is not symmetric.

Transitive:

$\sim$ is transitive iff whenever $(a, b) \sim (c, d) \hspace{2mm} \& \hspace{2mm} (c, d) \sim (e, f)$ then $(a, b) \sim (e, f)$

To prove transitivity let us assume $(a, b) \sim (c, d)$ and $(c, d) \sim (e, f)$ .

We have to show $(a, b) \sim (e, f)$

Since $(a, b) \sim (c, d)$ we have: $a^2 + b^2 \leq c^2 + d^2$

Since $(c, d) \sim (e, f)$ we have: $c^2 + d^2 \leq e^2 + f^2$

Combining both the inequalities we get:

$a^2 + b^2 \leq c^2 + d^2 \leq e^2 + f^2$

Therefore, we get: $a^2 + b^2 \leq e^2 + f^2$

Therefore, $\sim$ is transitive.

Hence, proved.

3 0

3 years ago

Heeeeeeeelllllpppp<br>why isnt anyone helping me :(<br>find MK

Ne4ueva [31]

Answer:

MK=32.5

Step-by-step explanation:

Hey There!

I believe that these triangles are similar

So to find MK we want to find the scale factor

To do this we divide

66/30=2.2

Now we want to divide 72.5 by 2.2

72.5/2.2=32.5

therefore MK=32.5

hope this helps!

8 0

3 years ago

Which expression is equivalent to -1/12x-1/3?

hichkok12 [17]

B. If you multiply 1/12 by (-x) it's -1/12x and if you multiply 1/12 by (-4) it's -4/12 which is equivalent to -1/3.

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3 years ago

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3 more than twice a number is 15 what is the number

vredina [299]

The number is 6 for this

4 0

3 years ago

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