Presentation on theme: "Dilations in the Coordinate Plane"— Presentation transcript:
1 Dilations in the Coordinate Plane EQ: How do you describe the properties of dilation?How can you describe the effect of dilation on coordinates using algebraic representation?What is the connection between transformation and similar figure?
2 DilationsDilationA transformation that changes the size of a figure. The original figure and transformed figure are similar.Corresponding angles are sameCorresponding side lengths are not same; but proportionalCenter of dilation - The point of projectionIn the coordinate plane, the center of dilation is the origin.
3 Enlargement Reduction Two types of dilations The dilation is a reduction if the scale factor is between 0 and 1.The dilation is an enlargement if the scale factor is > 1.
4 Dilations Scale factor - The amount of change written as a ratio To find the new coordinates, multiply the original coordinates by the scale factor.
5 Steps to Follow Plot the given points. Multiply each coordinate by the scale factor.Plot the image points.State the coordinates of the dilation.
6 Finding a Scale FactorThe blue triangle is a dilation image of the red triangle. Describe the dilation.The center is X. The image is larger than the preimage, so the dilation is an enlargement.
7 Finding a Scale FactorThe blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation.
8 Graphing Dilation Images ∆PZG has vertices P(2,0), Z(-1, ½), and G (1, -2).What are the coordinates of the image of P for a dilation with center (0,0) and scale factor 3?a) (5, 3) b) (6,0) c) (2/3, 0) d) (3, -6)
9 Algebraic Notation of Dilation In a coordinate plane, dilations whose centers are the origin have the property that the pre-image P to image P’ where ‘k’ is the scale factor.P (x, y) P’ (kx, ky)