+84 1)How many different lines of symmetry does a regular 11-gon have?
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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?
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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?
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9)In triangle XYZ, XY = 20, YZ = 15 and XZ = 25. Y is reflected over XZ to Yprime. Find YYprime.
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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.
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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?
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