Question

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

Answer 1

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.

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.

Answer 2

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.

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.