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1)How many different lines of symmetry does a regular 11-gon have?

Picture: https://latex.artofproblemsolving.com/8/4/4/84445c7f96e3f03517a1e8c2b67725eb69bfc74e.png

2)Point Q is the image of point P under a dilation with center O and scale factor 4. If PQ = 18, then what is OP?

3)A reflection maps A to B and B to C. Given AB = 12 find AC.

4)A dilation with scale factor -3 maps X to Xprime and Y to Yprime. Given XprimeYprime = 2, find XY.

5)A reflection maps A to B and C to C. If AB = 12, then what is the shortest possible length of AC?

6)When a square with area 4 is dilated by a scale factor of k we obtain a square with area 9. Find the sum of all possible values of k.

7)In triangle ABC, AB = BC = 5 and CA = 6.

Triangle ABC is first rotated clockwise about A for 90 degrees to triangle AB1C1.

Triangle AB1C1 is then reflected over B1C1 to triangle A1B1C1.

Triangle A1B1C1 is then translated 8 units to the right to triangle A2B2C2.

Triangle A2B2C2 is then dilated about A to triangle A3B3C3 with scale factor -4.

What is the perimeter of triangle A3B3C3?

Picture: https://latex.artofproblemsolving.com/e/6/9/e69e279ed1f8312a80941122afbf3d2a8b6b119a.png

8)D, E and F are the midpoints of BC, CA, and AB respectively. A dilation maps triangle ABC to triangle DEF. What is the scale factor of this dilation?

Picture: https://latex.artofproblemsolving.com/2/7/7/277eb9ff33baa2ebc2195fb52a18918053f002e0.png

9)In triangle XYZ, XY = 20, YZ = 15 and XZ = 25. Y is reflected over XZ to Yprime. Find YYprime.

Picture: https://latex.artofproblemsolving.com/4/7/d/47deb1d8e00693fe83789bc760cf9f4cef5a5013.png

10)As shown in the diagram, angle MOL = 30 degrees and A is a point inside angle MOL with OA = 6. Let B and C be points on rays OM and OL, respectively. Find the smallest possible perimeter of triangle ABC.

Picture: https://latex.artofproblemsolving.com/7/d/9/7d957ed179a1092b65680707dd356a356d05a02e.png

11)A laser is shot from vertex A of square ABCD of side length 1, towards point P on BC so that BP = 3/4. The laser reflects off the sides of the square, until it hits another vertex, at which point it stops. What is the length of the path the laser takes?

Picture: https://latex.artofproblemsolving.com/c/9/0/c904b038f475065d64d6dbc320b079311b9b2d2b.png

FiestyGeco Apr 29, 2018