A triangle has corners at #(1, 7 )#, #( 8, 3 )#, and #( 4 , 8 )#. If the triangle is dilated by # 2 x# around #(2, 5)#, what will the new coordinates of its corners be?
1 Answer
Feb 17, 2018
Explanation:
#"label the vertices of the triangle"#
#A(1,7),B(8,3)" and "C(4,8)#
#"and A', B', C' the images of A, B and C"#
#"let the centre of dilatation be "D(2,5)#
#rArrvec(DA')=color(red)(2)vec(DA)#
#rArrula'-uld=2(ula-uld)=2ula-2uld#
#rArrula'=2ula-uld#
#color(white)(rArrula')=2((1),(7))-((2),(5))=((0),(9))#
#"the coordinates of A' are the components of "ula'#
#rArrA'=(0,9)#
#"similarly "#
#vec(DB')=color(red)(2)vec(DB)#
#rArrulb'=2ulb-uld#
#color(white)(rArrulb')=2((8),(3))-((2),(5))=((14),(1))#
#rArrB'=(14,1)#
#"and "vec(DC')=color(red)(2)vec(DC)#
#rArrulc'=2ulc-uld#
#color(white)(rArrulc')=2((4),(8))-((2),(5))=((6),(11))#
#rArrC'=(6,11)#
#color(blue)"Result after dilatation"#
#(1,7)to(0,9),(8,3)to(14,1),(4,8)to(6,11)#
