Problems(2)
An architect is building a structure that will place vertical pillars at the vertices of regular hexagon ABCDEF, 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 A, B, and C are 12,9, and 10 meters, respectively. What is the height, in meters, of the pillar at E?<spanclass=′latex−bold′>(A)</span>9<spanclass=′latex−bold′>(B)</span>63<spanclass=′latex−bold′>(C)</span>83<spanclass=′latex−bold′>(D)</span>17<spanclass=′latex−bold′>(E)</span>123 Distinct lines ℓ and m lie in the xy-plane. They intersect at the origin. Point P(−1,4) is reflected about line ℓ to point P′, and then P′ is reflected about line m to point P′′. The equation of line ℓ is 5x−y=0, and the coordinates of P′′ are (4,1). What is the equation of line m?(<spanclass=′latex−bold′>A</span>)5x+2y=0(<spanclass=′latex−bold′>B</span>)3x+2y=0(<spanclass=′latex−bold′>C</span>)x−3y=0
(<spanclass=′latex−bold′>D</span>)2x−3y=0(<spanclass=′latex−bold′>E</span>)5x−3y=0