Could someone help me with this problem? I'm confused.

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Answer 1 · 2018-04-04T20:57:55

#C' = (-6,3)#

#m' = -3#

We know that point #A = (2,3)# and point #C = (0,3)#

The formula for a dilation factor of 4 for C with respect A is:

#C' = (4(C_x-A_x)+A_x, 4(C_y-A_y)+A_y)#

Substituting in the know values:

#C' = (4(0-2)+2, 4(3-3)+3)#

#C' = (4(-2)+2,4(0)+3)#

#C' = (-6,3)#

To obtain the slope we need to pick another point on the given line; I shall choose #B = (2,-3)#.

The formula for a dilation factor of 4 for B with respect A is:

#B' = (4(B_x-A_x)+A_x, 4(B_y-A_y)+A_y)#

Substituting in the known values:

#B' = (4(2-2)+2, 4(-3-3)+3)#

#B' = (4(0)+2, 4(-6)+3)#

#B' = (2, -21)#

We can use #C' and B'# to compute the slope of the new line:

#m' = (B'_y- C'_y)/(B'_x- C'_x)#

#m' = (-21- 3)/(2- -6)#

#m' = -24/8#

#m' = -3#