Dilations. Lesson 14.5 Pre-AP Geometry. Lesson Focus. There are transformations that do not preserve distance. This lesson introduces one such transformation, called a dilation. Basic Terms. Dilation
There are transformations that do not preserve distance. This lesson introduces one such transformation, called a dilation.
A transformation that changes the size of a figure by a scale factor to create a similar figure. A dilation is not rigid.
A dilation with a center O and a nonzero scale factor k maps any point P to a point P’.
1) If k > 0, P’ lies on and OP’ = k · OP.
2) If k < 0, P’ lies on the ray opposite and OP’ = |k| · OP.
A dilation where the scale factor |k| > 1.
A dilation where the scale factor |k| < 1.
A transformation that maps any geometric figure to a similar geometric figure.
A dilation is not an isometry as distances are not preserved.
A dilation maps a triangle to a similar triangle.
A dilation maps an angle to a congruent angle.
A dilation DO,k maps any segment to a parallel segment |k| times as long.
A dilation DO,k maps any polygon to a similar polygon whose area is k2 times as large.
Find: (a) DO,2 ; (b) DO, -1/3
2. A dilation with the origin, O, as center maps (3, 4) to (9, 12). Find the scale factor. Is the dilation an expansion or a contraction?
(-3, 4) → (1, -4/3). Find the scale factor.
Is the dilation an expansion or contraction?
a. the x-axis
b. the y-axis
c. the line y = x
Problem Set 14.5, p. 596: # 2 – 8 (even)