How to Find the Scale Factor of a Dilation on a Graph

The scale factor of a dilation is a measure of its rotational change. A negative dilation, on the other hand, produces smaller images. This is because a negative dilation means an image rotates 180o. This is a useful tool to determine the rotational change in a graph.


A graph shows the relationship between the scale factor and the volume of a dilated solid. For example, consider a prism whose volume is 5 cubic units. To create a graph, make a table with the values for each of the three dimensions and connect them using a smooth curve. The graph rises fairly steeply from (0,0).

If the center of the dilation is at the origin, the resulting triangle has coordinates of A’, B’, and C’. Multiply the resulting values by the scale factor. This will give you the dilation factor. Next, measure the horizontal and vertical distances between the dilated triangle and its origin.

If the dilation scale factor is two, then the triangle is dilated by a factor of two. The resulting triangle is the image of the original triangle ABC. The scale factor of a dilation is 2. The corresponding coordinates of a dilated triangle are A(3,3), B(5,3), and C(15,9).

A scale factor is a number that determines how much the object is enlarged or shrunk in size. The formula for calculating a scale factor is as follows: Dimension of the original shape / Dimension of the new shape. For example, a square with a dilated side has an increase of four units, whereas a square with a dillation of twelve units has decreased by one unit.

A scale factor is an index of the change in size in a unit. This number represents the size of the dilated image in relation to the original. When the scale factor is greater than one, the image will be larger. If the scale factor is smaller, the image will shrink.

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