Section 8.7 Dilations OBJECTIVE: TO UNDERSTAND DILATION IMAGES OF FIGURES BIG IDEAS:TRANSFORMATIONS COORDINATE GEOMETRY ESSENTIAL UNDERSTANDING: A SCALE.

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Presentation transcript:

Section 8.7 Dilations OBJECTIVE: TO UNDERSTAND DILATION IMAGES OF FIGURES BIG IDEAS:TRANSFORMATIONS COORDINATE GEOMETRY ESSENTIAL UNDERSTANDING: A SCALE FACTOR CAN BE USED TO MAKE A LARGER OR SMALLER COPY OF A FIGURE THAT IS ALSO SIMILAR TO THE ORIGINAL FIGURE MATHEMATICAL PRACTICE: LOOK FOR AND MAKE USE OF STRUCTURE

 Recall the transformations from the previous chapter  Reflection, Rotation, Translation and Glide-Reflection  Rigid Motion because the figures are congruent (same size and shape)  A dilation is not a rigid motion because it does not preserve the size of the figure. A dilation produces a pair of similar figures whose corresponding side lengths are proportional. The scale factor related to a dilation is equal to the ratio of distances between pairs of corresponding points  Dilations are use in multiple real-world areas, such as science, technology and photography. DILATION

 A DILATION with CENTER OF DILATION and SCALE FACTOR n, n>0, can be written as. A dilation is a transformation with the following properties:  The image of  For any other point  Dilations preserve angle measure DILATION

 The scale factor of a dilation is the _____________ of a length of the image to the corresponding length in the preimage, with the image length always in the numerator.  A dilation is an _________________________ if the scale factor is greater than 1.  A dilation is a _____________________ is the scale factor is between 0 and 1 SCALE FACTOR

EX 1: IDENTIFY THE DILATION AND FIND ITS SCALE FACTOR  A)  B)

EX 2: IDENTIFY THE DILATION AND FIND ITS SCALE FACTOR

 A)What are the coordinates of the vertices of after a dilation of k, centered at the origin? EX 3: FINDING A DILATION IMAGE

 B)What are the coordinates of the vertices of the figure after a dilation of k, centered at the origin? EX 3: FINDING A DILATION IMAGE

 Then find the values of the variables. EX 4: IDENTIFY THE DILATION AND FIND ITS SCALE FACTOR.

 5.Jessica has a photograph that is 4 inches high and 6 inches wide. She wants to enlarge the picture by a scale factor of What are the new dimensions of the photograph? FINDING A DILATION IMAGE

Mastery on L15 and 80+ on L14 MATH IXL L14 AND L15