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.
Aug 12, 2018

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

Explanation:

#"Since the centre of dilatation is the origin to obtain"#
#"the images of the given points we only require to"#
#"multiply the coordinates of the original points "#
#"by the scale factor"#

#A'=(-8xx1.5),(8xx1.5)=(-12,12)#

#B'=(4xx1.5),(-2xx1.5)=(6,-3)#

#C'=(2xx1.5),(2xx1.5)=(3,3)#

Kalyanam S.
Aug 13, 2018

New coordinates of A, B, C are

#(-12,12), (6,-3), (3,3)# respectively.

Explanation:

#A(-8,8), B (4, -2), C (2,2), O (0,0)#

Dilated by factor d = 1.5 about origin#

#A’ ((x),(y)) = d * A ((x),(y)) - (d-1) * O ((x),(y))#

#A’((x),(y)) = 1.5* ((-8),(8)) - 0.5 * ((0),(0))#

Coordinates of #A’(x,y) = (-12, 12)#

Similarly coordinates of B’(x,y) = (1.54, 1.5-2) = (6,-3)#

#C’(x,y) = (1.5*2, 1.5*2) = (3,3)#

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