MathDB

3

Part of 2011 AIME Problems

Problems(2)

Changed axes in coordinate system

Source:

3/18/2011
Let LL be the line with slope 512\tfrac{5}{12} that contains the point A=(24,−1)A=(24,-1), and let MM be the line perpendicular to line LL that contains the point B=(5,6)B=(5,6). The original coordinate axes are erased, and line LL is made the xx-axis, and line MM the yy-axis. In the new coordinate system, point AA is on the positive xx-axis, and point BB is on the positive yy-axis. The point PP with coordinates (−14,27)(-14,27) in the original system has coordinates (α,β)(\alpha,\beta) in the new coordinate system. Find α+β\alpha+\beta.
analytic geometryAMCAIMEgeometrygeometric transformationrotationgraphing lines
Angles in an arithmetic sequence [2011.II.3]

Source:

3/31/2011
The degree measures of the angles of a convex 18-sided polygon form an increasing arithmetic sequence with integer values. Find the degree measure of the smallest angle.
AMCAIMEarithmetic sequenceAIME II