The question is incomplete. Here is the complete question.
A triangle has vertices J(-3,8), K(7,-1) and L(-2,0). The triangle is dilated so that vertex K'has coordinates (21,-3). Which algebraic representation represents the dilation?
a) (3x,3y) ---> (x,y)
b) (3x,y) ---> (x,3y)
c) (x, 3y) ---> (3x,y)
d) (x,y) ---> (3x, 3y)
Answer: d) (x,y) ---> (3x, 3y)
Step-by-step explanation: DIlation is the process of creating a similar figure that has sides smaller or larger than the original. It is done by multiplying or dividing each side by a scale factor.
The triangle JKL is the original figure. The dilated triangle (J'K'L') is made by multiplying the original by a scale factor of 3:
Vertex K is point (7,-1). Multiplying by 3, we have vertex K':
x' = 7*3
x' = 21
y' = (-1)*3
y' = -3
point (21,-3)
A dilated figure is equally enlarged or dimished, which means the scale factor is equal to every point.
The dilated triangle will be: J'(-9,24) K'(21,-3) L'(-6,0)
The algebraic representation for the dilation is given by
(x,y) ---> (3x,3y)
which is alternative d.
