Introduction A figure is dilated if the preimage can be mapped to the image using a scale factor through a center point, usually the origin. You have been.

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Presentation transcript:

Introduction A figure is dilated if the preimage can be mapped to the image using a scale factor through a center point, usually the origin. You have been determining if figures have been dilated, but how do you create a dilation? If the dilation is centered about the origin, use the scale factor and multiply each coordinate in the figure by that scale factor. If a distance is given, multiply the distance by the scale factor. 1.1.2: Investigating Scale Factors

Key Concepts The notation is as follows: Dk(x, y) = (kx, ky). Multiply each coordinate of the figure by the scale factor when the center is at (0, 0). 1.1.2: Investigating Scale Factors

Key Concepts, continued 1.1.2: Investigating Scale Factors

Key Concepts, continued The lengths of each side in a figure also are multiplied by the scale factor. If you know the lengths of the preimage figure and the scale factor, you can calculate the lengths of the image by multiplying the preimage lengths by the scale factor. Remember that the dilation is an enlargement if k > 1, a reduction if 0 < k < 1, and a congruency transformation if k = 1. 1.1.2: Investigating Scale Factors

Common Errors/Misconceptions not applying the scale factor to both the x- and y- coordinates in the point improperly converting the decimal from a percentage missing the connection between the scale factor and the ratio of the image lengths to the preimage lengths 1.1.2: Investigating Scale Factors

Guided Practice Example 2 A triangle has vertices G (2, –3), H (–6, 2), and J (0, 4). If the triangle is dilated by a scale factor of 0.5 through center C (0, 0), what are the image vertices? Draw the preimage and image on the coordinate plane. 1.1.2: Investigating Scale Factors

Guided Practice: Example 2, continued Start with one vertex and multiply each coordinate by the scale factor, k. Dk = (kx, ky) 1.1.2: Investigating Scale Factors

Guided Practice: Example 2, continued Repeat the process with another vertex. Multiply each coordinate of the vertex by the scale factor. 1.1.2: Investigating Scale Factors

Guided Practice: Example 2, continued Repeat the process for the last vertex. Multiply each coordinate of the vertex by the scale factor. 1.1.2: Investigating Scale Factors

Guided Practice: Example 2, continued List the image vertices. 1.1.2: Investigating Scale Factors

Guided Practice: Example 2, continued Draw the preimage and image on the coordinate plane. 1.1.2: Investigating Scale Factors

Guided Practice: Example 2, continued ✔ 1.1.2: Investigating Scale Factors

Guided Practice: Example 2, continued http://www.walch.com/ei/00131 1.1.2: Investigating Scale Factors

Guided Practice Example 3 What are the side lengths of with a scale factor of 2.5 given the preimage and image to the right and the information that DE = 1, EF = 9.2, and FD = 8.6? 1.1.2: Investigating Scale Factors

Guided Practice: Example 3, continued Choose a side to start with and multiply the scale factor (k) by that side length. 1.1.2: Investigating Scale Factors

Guided Practice: Example 3, continued Choose a second side and multiply the scale factor by that side length. 1.1.2: Investigating Scale Factors

Guided Practice: Example 3, continued Choose the last side and multiply the scale factor by that side length. 1.1.2: Investigating Scale Factors

Guided Practice: Example 3, continued Label the figure with the side lengths. 1.1.2: Investigating Scale Factors

Guided Practice: Example 3, continued ✔ 1.1.2: Investigating Scale Factors

Guided Practice: Example 3, continued http://www.walch.com/ei/00132 1.1.2: Investigating Scale Factors