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ale4655 [162]
2 years ago
5

How do you find the center of dilation for a negetive dilation?​

Mathematics
2 answers:
worty [1.4K]2 years ago
6 0

Answer:

Let's review a dilation takes a segment not going through the center to a parallel line and a segment going through the center to the same. Line. In this diagram. You see segment a b is the pre-image.

Step-by-step explanation:

And negative 12 negative 10 is located right here. After locating your Center dilation you must determine its distance to each of the three points of the triangle. You could use the Pythagorean theorem to calculate this distance. And then the long distance. But what you see is is that the corresponding. The point is now twice as far from your center of dilation. Just consider for a moment what would happen if you enlarge the by the scale factor of 2. Okay. So for instance, if I wanted to enlarge this point basic electro two I went one to the left and one down. Because I'm multiplying by one and a half I'm going to go along. Or down one and a half so this now becomes a flash. Lines drawn through each point on the pre-image and its corresponding image point will intersect at the center of dilation. When the origin is the center of dilation, each point on the pre-image (x,y) corresponds to (kx, ky). The way to do this when it's centered at the origin is just to multiply the coordinates of your original. Figure by the scale factor.

To find the scale factor for a dilation, we find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image. The ratio of these distances gives us the scale factor, as Math Bits Notebook accurately states.

Scale Factor: The scale factor in a dilation is the amount by which the figure is stretched or shrunk. Center of Dilation: The center of dilation is a reference point used to appropriately scale the dilation of a figure.

What happens if we dilate an entire line? If that line passes through the point which is the center of the dilation, nothing will change. Remember that the image point formed by a dilation will lie on a straight line connecting the pre-image point to the center of the dilation.

To find a scale factor between two similar figures, find two corresponding sides and write the ratio of the two sides. If you begin with the smaller figure, your scale factor will be less than one. If you begin with the larger figure, your scale factor will be greater than one.

The sides of the triangles adjacent to the center of dilation will be collinear. The third side of the preimage and image will be parallel. The vertex used as the center of dilation will be in the same location in both triangles.

Andrei [34K]2 years ago
5 0

the Answer:

Notice that the "image" triangles are on the opposite side of the center of the dilation (vertices are on opposite side of O from the preimage). Also, notice that the triangles have been rotated 180º.

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. The center of dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

Note:

A dilation is NOT referred to as a rigid transformation (or isometry) because the image is NOT necessarily the same size as the pre-image (and rigid transformations preserve length).

What happens when scale factor k is a negative value?

If the value of scale factor k is negative, the dilation takes place in the opposite direction from the center of dilation on the same straight line containing the center and the pre-image point. (This "opposite" placement may be referred to as being a " directed segment" since it has the property of being located in a specific "direction" in relation to the center of dilation.)

Let's see how a negative dilation affects a triangle:

Notice that the "image" triangles are on the opposite side of the center of the dilation (vertices are on opposite side of O from the preimage). Also, notice that the triangles have been rotated 180º.

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2(2x + 3) = -6(x + 9)
sergeinik [125]

Answer:

Your answer is -6.

Step-by-step explanation:

Simplify 2(2x+3) to get 4x+6  

Then simplify -6(x+9) to get -6x-54

Now you have 4x+6=-6x-54

Move all of the coefficients to one side:

10x+6=-54

Move all of the constants to the other side:

10x=-60

Divide each side by 10:

10/10x=-60/10

To get your answer of -6.

6 0
2 years ago
PLZZZZ ANSWER THIS..
slamgirl [31]

Answer:

In 3 - 5:  

3 + (-5), and -5 + 3

In 5 - 3:

5 + (-3), and -3 + 5

Step-by-step explanation:

Category : 3 - 5

Values must equal -2

3 + (-5) = 3 - 5 = -2

-5 + 3 = -2

Category : 5 - 3

Values must equal 2

5 + (-3) = 5 - 3 = 2

-3 + 5 = 2

If my answer is incorrect, pls correct me!

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2 years ago
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F(x) = 9 + 4x f(0) = f(-1) = Find the value of x for which f(x) =6 x=
puteri [66]

Answer: x=-3/4

Step-by-step explanation:

Since we know f(x)=6, we can set it equal to the equation.

6=9+4x           [subtract 9 on both sides]

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x=-3/4

8 0
3 years ago
at Michaels auto shop, it takes him 15 minutes to do an oil change and 24 minutes to do a tire change. let x be the number of oi
Roman55 [17]

Answer:

Step-by-step explanation:

At Susan's auto shop, it takes her 12 minutes to do an oil change and 18 minutes to do a tire change. Let x be the number of oil changes she does. Let y be the number of tire changes she does.

Using the values and variables given, write an inequality describing how many oil changes and tire changes Susan can do in less than 3 hours (180 minutes).

Answer provided by our tutors

The total time that Susan needs to change x oil changes and y tire changes is less than 180 min.

The time needed for x oil changes is 12 * x.

The time needed for y tire changes is 18 * y.

The total time is the sum of the above times and needs to be less than 180 that is

12 * x + 18 * y < 180 divide both sides of equation by 6

12/6 * x + 18/6*y < 180/6

2*x + 3*y < 30

2*x < 30 - 3*y divide both sides by 2 to get the inequality for x

x < 30/2 - 3/2*y = 15 - 1.5 y < 15 that is x < = 15

2*x + 3*y < 30

3*y < 30 - 2*x divide both sides by 3 to get the inequality for y

y < 30/3 - 2/3 *x = 10 - 2/3*x < 10 that is y < = 10

Also we can write x + y < x+ 3/2 * y < 15.

Susan can do not more then 5 oil changes and not more then 10 tire changes or all together she can do not more then 15 total of oil and tire changes.

Just do this problem but with Michael

8 0
2 years ago
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