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

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1 Answer
Apr 4, 2018

C' = (-6,3)

m' = -3

Explanation:

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