wat is dilation in math during moving or changing a figure
In mathematics, dilation is a transformation that resizes a geometric figure. It involves changing the size of the figure while keeping its shape intact. Specifically, dilation involves scaling up or down the figure by a certain factor called the scale factor.
To understand dilation, consider a simple example of a dilation by a scale factor of 2. Imagine a square on a coordinate plane with its vertices at (0, 0), (1, 0), (1, 1), and (0, 1). To dilate this square, we multiply the coordinates of each vertex by the scale factor (2). This will result in a new square with its vertices at (0, 0), (2, 0), (2, 2), and (0, 2). The sides of the new square are twice as long as the original square, but the angles remain the same.
Generally, to perform a dilation, you would follow these steps:
1. Identify the center of dilation: This is the point about which the figure will be resized. The center of dilation can be any point.
2. Determine the scale factor: The scale factor specifies how much the figure will be resized. It can be greater than 1 to enlarge the figure or between 0 and 1 to shrink it.
3. Multiply the coordinates of each vertex by the scale factor: This is done by multiplying the x-coordinate and the y-coordinate of each vertex by the scale factor. This will give you the new coordinates for the dilated figure.
4. Connect the new coordinates: Once you have the new coordinates, connect them in the same order they were connected in the original shape. This will give you the dilated figure.
Keep in mind that dilation can also be performed by changing the size of an object on paper using a ruler and a compass. In this case, you would measure the distance from the center of dilation to each point on the original figure, and then use the scale factor to determine the corresponding distances for the new figure.
I hope this explanation helps you understand dilation in math! Let me know if you have any further questions.