A triangle has corners at #(5, 8 )#, #( 3, 1 )#, and #( 9 , 2 )#. If the triangle is dilated by # 3 x# around #(4, 2)#, what will the new coordinates of its corners be?

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Answer 1 · 2018-02-20T08:22:33

New coordinates are

#A’ ((7),(20)), B’ ((1),(-1)), C’ ((19),(2))#

#A (5,8), B(3,1), C(9,2)#

Dilated around D(4,2) by a factor of 3.

#vec(AD) = 3 * vec(AB)#

#A’ = 3A - 2D = 3((5),(8)) - 2((4),(2)) = ((15),(24)) - ((8),(4)) = ((7),(20))#

#B’ = 3B - 2D = 3((3),(1)) - 2((4),(2)) = ((9),(3)) - ((8),(4)) = ((1),(-1))#

#C’ = 3C - 2D = 3((9),(2)) - 2((4),(2)) = ((27),(6)) - ((8),(4)) = ((19),(2))#