How can you determine the coordinates of any image that is dilated with the center of dilation at the origin without graphing? Explain your reasoning.

Please help

To determine the coordinates of any image that is dilated with the center of dilation at the origin without graphing, you can use the concept of dilation. Dilation is a transformation that scales an object by a factor called the scale factor.

When the center of dilation is at the origin, the scale factor determines how the image is expanded or contracted.

Here's how you can determine the new coordinates of a point after dilation:

1. Identify the original coordinates of the point, let's say (x, y).
2. Multiply both the x-coordinate and the y-coordinate by the scale factor.
- If the scale factor is greater than 1, the image will be expanded. Multiply both x and y by the scale factor to find the new coordinates.
- If the scale factor is between 0 and 1, the image will be contracted. Multiply both x and y by the scale factor to find the new coordinates.
- If the scale factor is negative, the image will be reflected. Multiply both x and y by the absolute value of the scale factor to find the new coordinates, but keep the signs of the original coordinates.
3. The new coordinates of the point after dilation are (scale factor * x, scale factor * y).

For example, let's say we have a point with original coordinates (3, -2), and the scale factor is 2. To find the new coordinates after dilation:

New x-coordinate = 2 * 3 = 6
New y-coordinate = 2 * -2 = -4

So the new coordinates after dilation would be (6, -4).

By following this process, you can determine the coordinates of any image that is dilated with the center of dilation at the origin without graphing.

for a point (x,y) , a dilation of factor f (centered at the origin)

will result in a new point [(x * f),(y * f)]