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?

Answer 1

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.