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Problems(2)

A weird solar panel

Source: 2021 AMC 10A (Fall) #17

11/11/2021
An architect is building a structure that will place vertical pillars at the vertices of regular hexagon ABCDEFABCDEF, which is lying horizontally on the ground. The six pillars will hold up a flat solar panel that will not be parallel to the ground. The heights of the pillars at AA, BB, and CC are 12,9,12,9, and 1010 meters, respectively. What is the height, in meters, of the pillar at EE?
<spanclass=latexbold>(A)</span>9<spanclass=latexbold>(B)</span>63<spanclass=latexbold>(C)</span>83<spanclass=latexbold>(D)</span>17<spanclass=latexbold>(E)</span>123<span class='latex-bold'>(A) </span>9\qquad<span class='latex-bold'>(B) </span>6\sqrt3\qquad<span class='latex-bold'>(C) </span>8\sqrt3\qquad<span class='latex-bold'>(D) </span>17\qquad<span class='latex-bold'>(E) </span>12\sqrt3
Transformation Problem (10B #17)

Source:

11/17/2021
Distinct lines \ell and mm lie in the xyxy-plane. They intersect at the origin. Point P(1,4)P(-1, 4) is reflected about line \ell to point PP', and then PP' is reflected about line mm to point PP''. The equation of line \ell is 5xy=05x - y = 0, and the coordinates of PP'' are (4,1)(4,1). What is the equation of line m?m?
(<spanclass=latexbold>A</span>)5x+2y=0(<spanclass=latexbold>B</span>)3x+2y=0(<spanclass=latexbold>C</span>)x3y=0(<span class='latex-bold'>A</span>)\: 5x+2y=0\qquad(<span class='latex-bold'>B</span>) \: 3x+2y=0\qquad(<span class='latex-bold'>C</span>) \: x-3y=0 (<spanclass=latexbold>D</span>)2x3y=0(<spanclass=latexbold>E</span>)5x3y=0(<span class='latex-bold'>D</span>) \: 2x-3y=0\qquad(<span class='latex-bold'>E</span>) \: 5x-3y=0