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Connect similarity, trigonometry, and coordinate geometry
Worksheet
Grade Level
Geometry
GEO.103 Connect similarity, trigonometry, and coordinate geometry
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A dilation centered at the origin maps Q(5,-12) to P(15,-36). Which setup gives the scale factor and the tangent ratio that stays unchanged?
A
Use ratio: 15/5 = -36/-12 = 3, and tan(theta) = -12/5
B
Use distance: OP = 39, so scale factor is 39 and tan(theta) = 39/15
C
Use slope: (-36 + 12)/(15 - 5) = -12/5, so scale factor is -12/5
D
Use ratio: 5/15 = -12/-36 = 3, and tan(theta) = 5/-12
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