Rebecca is designing a parking lot. A tall light will illuminate the three entrances, at A, B and C. Rebecca needs to position the lamp so that it illuminates.

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Presentation transcript:

Rebecca is designing a parking lot. A tall light will illuminate the three entrances, at A, B and C. Rebecca needs to position the lamp so that it illuminates each entrance equally. A(-8, 14) B(-4, 8) C(18, 10) How can Rebecca determine the location of the lamp?

A(-8, 14) B(-4, 8) C(18, 10) We are looking for the circumcenter since this is the point that is an equal distance from each vertex. We need to draw 3 perpendicular bisectors and find where they intersect – this is the circumcenter 1 2 3

A(-8, 14) B(-4, 8) C(18, 10) We can use the point (7, 9) to find b: y 2 = -11x + b 9 = -11(7) + b 9 = b b = 86 Therefore the equation of the perpendicular bisector of BC is y 2 = -11x + 86

Power line Cable Lamp (6, 19) (12, 10) (0, 4) The cable is perpendicular to the power line, so the slope of the cable is -2. An equation for the perpendicular line is y = -2x + b A point on the line is (6, 19): 19 = -2(6) + b 19 = b b = 31 y = -2x + 31

Power line Cable Lamp (6, 19) (0, 4)