Triangle ABC maps to triangle A′B′C′ by a 90∘ rotation counterclockwise about the origin.

If AB=61 units, BC=11 units, and AC=60 units, what is the length of A′C′?
11 units
61 units
90 units
60 units

Answers

Answer 1

Answer:

60 Units

Step-by-step explanation:

The length of AC does not change. Since the translation is a rotation, nothing about the size of the triangle should change. Meaning A'B'C' is still 60 units in length.

Answer 2

The length of the side A'C' of the triangle after rotation is A'C' =AC = 60 units

What is Rotation?

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the triangle be represented as ΔABC

Now , the measures of the sides of the triangle are

The measure of side AB = 61 units

The measure of side BC = 11 units

The measure of side AC = 60 units

And , the triangle is rotated by 90° counterclockwise  about the origin

The coordinates of the triangle after rotation is A'B'C'

And ,

The measure of side A'B' = 61 units

The measure of side B'C' = 11 units

The measure of side A'C' = 60 units

The length of the sides of the triangle does not change during a transformation of rotation by any degree

Hence , the measure of side A'C' of triangle is 60 units

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Related Questions

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Which expression is equivalent to -12(3x-3/4)

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Answers

Answer:

Last one, -36x+9.

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at a football game, every person is either a fan of the home team or of the visiting team. omar observes that the ratio of fans of the home team to fans of the visiting team is 7:2. omar states that the total number of fans at the game must be an odd number because 7 + 2 = 9 and 9 is an odd number.

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Answers

Answer:

294

Step-by-step explanation:

surface area of a cube = 6* a^2

6 * 7^2

= 6* 49

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Answer:

Step-by-step explanation:

pi r^2 for area

pi 35^2

pi1225= about 3848.45

2pi r for circumference

2pi35

pi70= about 219.9

Factor the expression (x+4)^2-4y^5(x+4)+4y^10

Answers

if you factor this,
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Out of 180 students, 50 students play Piano, 68 play Guitar, and 59 play Flute
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Draw a Venn diagram to represent this information.

Answers

Answer:

Step-by-step explanation:

A Venn diagram depicts the logical relationships between two or more sets of elements by using alternating circles or other shapes. They're often used to visually arrange information, showing how objects are similar and different. In the fields of mathematics and statistics, Venn diagrams, also known as "set diagrams" or "logic diagrams," are commonly used.

From the given information:

Since we are to represent the given question into a Venn diagram, the diagram is being attached in the image below.

From the image below, we represent:

P =students that played Paino

G = students that played guitar

F = students that played flute

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G = 68

F = 59

(PUG) -35

(PUF) = 59

(GUF) = 40

since the value of (PUGUF) is not given, we represent it with x.

See the attached image below for diagrammatic representation of the Venn diagram.

Which graph represents a direct variation?

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I don't know all of them I guess since I can't see the graphs

Answer:

The graph of the direct variation equation is a straight line through the origin.

Step-by-step explanation:

Find the value of x.

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What is an equation of the line that passes through the point (-5,-2) and is
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Answers

Answer:

[tex]y=x+3[/tex]

Step-by-step explanation:

What we need to know

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines have the same slope

1) Rewrite the equation x - y = 5 into slope-intercept form and identify the slope

[tex]x - y = 5[/tex]

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[tex]x - y -x= -x+5\\-y= -x+5[/tex]

Divide both sides by -1

[tex]y= x-5[/tex]

Now, we can tell clearly that the slope (m) of this line is 1. Therefore, a line parallel to this would also have a slope of 1.

Plugging 1 as m into [tex]y=mx+b[/tex], we get:

[tex]y=x+b[/tex]

2) Find the y-intercept (b) of the line parallel to [tex]y= x-5[/tex] and find the final equation

[tex]y=x+b[/tex]

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[tex]-2=-5+b[/tex]

Add 5 to both sides

[tex]-2+5=-5+b+5\\3=b[/tex]

Therefore, the y-intercept of this line is 3. Now, plugging this back into our original equation, we get:

[tex]y=x+b\\y=x+3[/tex]

I hope this helps!

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Answers

Answer:

38

Step-by-step explanation:

what is the name of the shape depicted in the graph below
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d. lemniscate

Answers

Answer:

Limaçon

Step-by-step explanation:

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The name of the shape depicted in the graph below is a. Limacon.

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It is the 2nd one you’re welcome

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Step-by-step explanation:

5 rubber stamps cost $9.70.
Which equation would help determine the cost of 11 rubber stamps?
A: x/11 = 5/9.70
B: 11\$9.70 = x/5
C: 5/11 = x/9.70
D: 11/5 = 9.70/x
E: None of the above

Answers

E None of the above

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In a test of hypothesis for a mean, which statement is CORRECT?

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The population distribution can be any distribution because the sample mean is always Normally distributed.
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Answers

Answer:

As long as the population distribution consists only of positive values, sample size does not matter.

Step-by-step explanation:

As long as the population distribution consists only of positive values, sample size does not matter.

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Answers

Answer:

A.

x + 2 + 12

Step-by-step explanation:

Thomas (t) = Andrew (x) * 2 + 12

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Answers

Answer: $46.08

Step-by-step explanation:

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Answers

Step-by-step explanation:

88 X 0,15 =....

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=[tex]\frac{mv^{2} }{2}[/tex] ; Solve for v.

Answers

Answer:

[tex]v=\sqrt{\frac{2E}{m} }[/tex]

Step-by-step explanation:

[tex]E=\frac{mv^2}{2}[/tex]

[tex]2E=mv^2}[/tex]

[tex]v^2=\frac{2E}{m}[/tex]

[tex]v=\sqrt{\frac{2E}{m} }[/tex]

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Answers

Answer:

The answer to this problem is 12.5.

Step-by-step explanation:

The formula for finding the area of a triangle is b * h * 1/2 or divide by 2 (base times height times one-half or two).

Since this is a equilateral triangle, all of the sides are equivalent to each other.  Since we know one of the sides is 5, all of the sides are 5.

5 * 5 = 25

Then you need to multiply this answer by 1/2 or divide by 2, whichever is easier.

25 / 2 = 12.5

The answer is 12.5.

Also, it would be FANTABULOUSLY AMAZING if I could get brainliest!!!

Just sayin, that would be pretty great.

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Answers

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Answers

If I’m not wrong it’s one solution because the sum of 3(x-1)+5=3x+2 is 0

Hope this helps!

Can you figure out the missing number​

Answers

Answer:

probably 6 thats one of the missing ones

ANSWER ASAP PLS

The circular opening of a tunnel has a circumference of 36 meters. Which equation can be used to find d, the
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Answers

D = circumference divided by Pi

D = 36 divided by 3.14

D = 11.5

ANSWER THE QUESTION FOR BRAINLIEST

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Non linear means not a straight line so answer C or the third answer.

Answer:

not a straight line

Step-by-step explanation:

Linear has the word "line" in it. A linear relation has a graph shaped like a straight line.

Nonlinear means "not like a straight line".

Answer: not a straight line

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