1. 14 – 5 Dilations. A dilation D O, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image |k| > 1 is an EXPANSION, expands the picture |k| < 1 is a CONTRACTION, shrinks the picture P O CenterScale factor

2. A dilation D O, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image |k| > 1 is an EXPANSION, expands the picture |k| < 1 is a CONTRACTION, shrinks the picture A O 1) Draw a line through Center and vertex. 2) Extend or shrink segment by scale factor. (Technically by construction and common sense) 3) Repeat, then connect. B C A` B` C`

3. A dilation D O, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image |k| > 1 is an EXPANSION, expands the picture |k| < 1 is a CONTRACTION, shrinks the picture A O B C A` B` C`

4. A dilation D O, k maps any point P to a point P`, determined as follows: 1) If k > 0, P` lies on OP and OP` = |k|OP 2) If k<0, P` lies on the ray opposite OP and OP` = |K|OP 3) The center is its own image |k| > 1 is an EXPANSION, expands the picture |k| < 1 is a CONTRACTION, shrinks the picture A O B C A` B` C` If you notice, a negative k in a way rotates the picture

5. Theorem 14 – 5: A dilation maps any triangle to a similar triangle. Cor 1: A dilation maps an angle to a congruent angle. Cor 2: A dilation D o,k maps any segment to a parallel segment |k| times as long Cor 3: A dilation D o,k maps any polygon whose area is k 2 times as large. Let’s discuss some justification here, types of invariancy.

6. A O B C O A B C

7. Remember, different slides for different periods. F - HW #70: Pg 590: 31, 32, 34, 35, 36. Pg 596: 6—14 even, 15—19, 22, 23, 25, 26

8. 0 period, 3 points curve, 2 for Ch 8, 1.5 for Ch 9. 6.5 total.

9. 4 th period, curve, 5. 2 pts for a mistake, 2 points for curve.