Geometry 9.7a, Dilations: Identify, Construct, & draw on a coordinate plane

An explanation of how a dilation is a transformation that changes the size of a figure but not the shape. How the image and preimage of a figure under dilation are similar, constructing a dilation with a compass and straightedge, how the scale factor k of a dilation is the ratio of a linear measurement of the image to a corresponding measurement of the preimage. We discuss how a dilation enlarges or reduces all dimensions proportionally by a scale factor k, that if k is greater than 1 it will equal an enlargement and if k is greater than 0 but less than 1 it will equal a reduction. An example is given of having a scale factor of 12 for a drawing in a sketchbook to become a wall mural, then finding the perimeter of the wall mural. We discuss dilations in the coordinate plane as P (x,y) with scale factor k becomes P'(kx,ky). What happens when a scale factor is the inverse of k, as -k. We draw a dilation in the coordinate plane with a scale factor -2 centered at the origin, and how we can use multiplication of a scalar to find the coordinates of the vertices of that dilation.

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