Triangle ABC has coordinates of A(-8, -8), B(4, -2), and C(2, 2). What are the coordinates of its image after a dilation centered at the origin with a scale factor of 1.5?

2 Answers
Jim G.
Apr 10, 2018

#(-12,-12),(6,-3)" and "(3,3)#

Explanation:

#"let A', B' and C' represent the image of A, B and C"#

#rArrvec(OA')=color(red)(1.5)vec(OA)#

#color(white)(rArrvec(OA'))=1.5((-8),(-8))=((-12),(-12))#

#rArrA'(-12,-12)#

#rArrvec(OB')=color(red)(1.5)vec(OB)#

#color(white)(rArrvec(OB'))=1.5((4),(-2))=((6),(-3))#

#rArrB'(6,-3)#

#rArrvec(OC')=color(red)(1.5)vec(OC)#

#color(white)(rArrvec(OC'))=1.5((2),(2))=((3),(3))#

#rArrC'(3,3)#

CW
Apr 10, 2018

see explanation.

Explanation:

enter image source here
A dilation that creates a larger image is called an enlargement (scale factor #k > 1#).
A dilation that creates a smaller image is called a reduction (#0 < k < 1#).
After a dilation centered at the origin with a scale factor of #+k#,
a point #A(x,y) -> A'(kx,ky)#
given that #k=1.5#,
#=> A(-8,-8) -> A'(1.5xx(-8), " "1.5xx(-8))=A'(-12,-12)#
#B(4,-2) -> B'(1.5xx4, " "1.5xx(-2))=B'(6,-3)#
#=> C(2,2) -> C'(1.5xx2, " "1.5xx2)=C'(3,3)#

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