Mathematics, 11.03.2020 16:51 Hockeypro1127

Which of these sequences of transformations would not return a shape to its original position? *
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Translate 3 units up, then 3 units down.
Reflect over line p , then reflect over line p again.
Translate 1 unit to the right, then 4 units to the left, then 3 units to the right.
Rotate 120 degrees counterclockwise around center C , then rotate 220 degrees counterclockwise around C again

Answers: 2

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Answer from: lae270

Transformation involves changing the position of a shape.

The transformation that would not return a shape to its original position is:

Rotate

counterclockwise around center C, Rotate 220^o

counterclockwise around C again

(a) Translate 3 units up, then 3 units down

Up and down translations are direct opposite translations.An upward movement by 3 units would be cancelled by a downward movement of 3 units, and the shape will return to its original position

(b) Reflect over line p, twice

Reflections over the same line in an even-number times will cancel out each other.A reflection over line p twice, will return the shape to its initial position

Right and left translations are direct opposite translations.

We have:

Left = 4

Right = 1 + 3 = 4

A 4 units movement in the right direction would be cancelled by a 4 units movement in the left directionThe shape will return to its original position

(d) Rotate 120^o counterclockwise around center C, then rotate 220^o counterclockwise around C again

The first rotation is given as:

$\theta_1 = 120^o$ -- counterclockwise

The second rotation is given as:

$\theta_2 = 220^o$ -- counterclockwise

The total rotation is calculated as:

$\theta = \theta_1 +\theta_2$

$\theta = 120^o + 220^o$

$\theta = 340^o$

This means that the shape is rotated 340^o counterclockwise.

For the shape to return to its original location, it must be rotated 360^o counterclockwise.

Hence, option (d) is correct

Read more about transformations at:

link

Answer from: charlesrogers38

4.Rotate 120 degrees counterclockwise around center C , then rotate 220 degrees counterclockwise around C again

Step-by-step explanation:

We have the following statements:

1.Translate 3 units up, then 3 units down.

Translating a graph 3 units up , and then 3 units down will counter cancel each other . Original position returned here!

2.Reflect over line p , then reflect over line p again.

Reflecting over line p , and then again reflecting over p , counter cancelling each other . Original position returned here!

3.Translate 1 unit to the right, then 4 units to the left, then 3 units to the right.

Translating 1 unit right and 4 units left i.e. move 3 left units then 3 units right which counter cancel each other . Original position returned here!

4.Rotate 120 degrees counterclockwise around center C , then rotate 220 degrees counterclockwise around C again

Rotating 120 degrees counterclockwise around center C , then rotating 220 degrees counterclockwise around C again will let it differ from 340 degrees from original position . Here , these sequences of transformations would not return a shape to its original position.

Answer from: Quest

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

Answer from: Quest

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.