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12-1 Size Transformations Revisited

12-1 Size Transformations Revisited. 12-1 Size Transformations Revisited. Size transformations can be accomplished with any point as center and do not require coordinate geometry. 12-1 Size Transformations Revisited.

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12-1 Size Transformations Revisited

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  1. 12-1 Size Transformations Revisited

  2. 12-1 Size Transformations Revisited Size transformations can be accomplished with any point as center and do not require coordinate geometry.

  3. 12-1 Size Transformations Revisited Seven dolls are pictured on page 717. The widths of their faces, measured across the widest part, are shown in table below. If the face of the sixth-largest doll (front row second from the right) is viewed as having a width of 1 unit, what are the widths of the faces of the other 6 dolls? Round the answers to the nearest thousandth.

  4. 12-1 Size Transformations Revisited Definitions of Size Change (Size Transformation) with Any Center, Magnitude, and Size-Change Factor Let O be a point and k be any nonzero real number. For any point P, let S(P) = P’ be the point on lineOP with OP’ = k · OP in the direction of rayOP if k is positive and in the direction opposite rayOP if k is negative. Then S is the size change or size transformation with center O and magnitude or size-change factor k.

  5. 12-1 Size Transformations Revisited

  6. 12-1 Size Transformations Revisited Theorem The transformation Skthat maps (x, y) onto (kx, ky), with k ¹ 0, is a size transformation S with center (0, 0) and magnitude k.

  7. 12-1 Size Transformations Revisited Size-Change Preservation Properties Theorem Every size transformation preserves: • angle measure • betweenness • collinearity.

  8. 12-1 Size Transformations Revisited Suppose S is a size transformation of magnitude 0.45. If DMNP has a perimeter of 84 centimeters, find the perimeter of S(DMNP).

  9. 12-1 Size Transformations Revisited Find the lengths of the sides and the area of DPQR with vertices P = (1, 1), Q = (8, 1), and R = (8, 5). Now find the lengths of the sides and the area of DXYZ if the transformation S3, with center (0, 0), maps DPQR onto DXYZ.

  10. 12-1 Size Transformations Revisited Figure Size-Change Theorem If a figure is determined by certain points, then its size-change image is the corresponding figure determined by the size-change images of those points.

  11. 12-1 Size Transformations Revisited Let’s explore the transformation Sm, nthat maps (x, y) onto (mx, ny). • a. What is the slope of the image of the line y = x under Sm, n? • b. If a figure has area A, what is the area of the image of that figure if each point is transformed by Sm, n? • c. What is an expression for the length of the segment whose endpoints are (a, b) and Sm, n(a, b)?

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