The scale factor can either increase the size of an object or decrease the size of an object. The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
How do you identify a dilation?
A description of a dilation includes the scale factor (or ratio) and the center of the dilation. The center of dilation is a fixed point in the plane. If the scale factor is greater than 1, the image is an enlargement (a stretch). If the scale factor is between 0 and 1, the image is a reduction (a shrink).
What is a dilation in geometry?
A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor, k. The value of k determines whether the dilation is an enlargement or a reduction. Simply, dilations always produce similar figures.
How do you find a scale factor?
The basic formula to find the scale factor of a figure is: Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape. This can also be used to calculate the dimensions of the new figure or the original figure by simply substituting the values in the same formula.
How do you find a scale factor with coordinates?
If the center of dilation is the origin, then the coordinates are multiplied by the scale factor: (x,y) -> (kx, ky) where k is the scale factor. To solve a problem like the one you presented, determine the scale factor by dividing the coordinates of X’ by the corresponding coordinates of X.
What is a dilation factor in math?
A dilation is a type of transformation that changes the size of the image. The scale factor, sometimes called the scalar factor, measures how much larger or smaller the image is. Below is a picture of each type of dilation (one that gets larger and one that gest smaller).
How do you find the dilation using the scale factor?
To dilate something in the coordinate plane, multiply each coordinate by the scale factor. This is called mapping. For any dilation the mapping will be (x,y)→(kx,ky). In this text, the center of dilation will always be the origin.