A triangle has corners at #(4, 5 )#, #( 4, 3 )#, and #( 4 , 2 )#. If the triangle is dilated by # 2 x# around #(1, 0)#, what will the new coordinates of its corners be?

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Answer 1 · 2018-02-12T12:00:55

New coordinates of the corners are #color(blue)(A' (7,10), color(blue)(B' (7,6),color(blue)(C' (7,4)#

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Given : A (4,5), B (4,3), C(4,2)

Dilated about D(1,0) and dilation factor 2

To find the new coordinates of the corners

#vec(A'D) = 2 * vec(AD)#

#a' - d = 2(a - d)# or #a' = 2a - d#

#=> 2((4),(5)) - ((1),(0)) = ((7),(10))#

#color(blue)(A' (7,10)#

#vec(B'D) = 2 * vec(BD)#

#b' - d = 2(b - d)# or #b' = 2b - d#

#=> 2((4),(3)) - ((1),(0)) = ((7),(6))#

#color(blue)(B' (7,6)#

#vec(C'D) = 2 * vec(CD)#

#c' - d = 2(c - d)# or #c' =2c - d#

#=> 2((4),(2)) - ((1),(0)) = ((7),(4))#

#color(blue)(C' (7,4)#