In the previous posts, we learned about dilations and scale factors. Now, let's explore how to apply dilations to figures on a coordinate plane. Suppose we have a figure with coordinates (x, y) and we want to dilate it by a scale factor of k. To dilate a figure on a coordinate plane, we multiply the x-coordinate and the y-coordinate of each point by the scale factor. For example, if we have a point (3, 5) and we want to dilate it by a scale factor of 2, we will get (6, 10). Let's consider another example. If we have a triangle with vertices (2, 4), (6, 4), and (4, 8), and we want to dilate it by a scale factor of 1/2, the new triangle will have vertices (1, 2), (3, 2), and (2, 4).

When dilating a figure on a coordinate plane, it is important to remember that the center of dilation acts as the fixed point. For instance, if the center of dilation is the origin (0, 0), then the origin remains unchanged. However, if the center of dilation is a point other than the origin, all other points move closer or farther away from that center, depending on the scale factor.

Dilations on a coordinate plane can be represented visually using graphs or grids. By plotting the original figure and the dilated figure, we can observe the transformation. The dilated figure will have similar proportions to the original figure, but its size will be either larger or smaller, depending on the scale factor. It's important to note that the shape and orientation of the figure remain the same, only the size changes.

Now that we understand how to dilate figures on a coordinate plane, let's practice some examples to solidify our understanding. Remember to always consider the scale factor and the center of dilation when dilating a figure. Keep practicing, and you'll master dilations in no time! You've got this!