A line segment has endpoints at (2 ,8 ) and (2 , 1). The line segment is dilated by a factor of 3 around (6 , 4). What are the new endpoints and length of the line segment?

1 Answer
Feb 5, 2018

Two end points are A' = color(brown)(-6, 16), B' = = color(brown)(-6, -5)

Length of the line segment using distance formula,vec(A'B') = color(green)(21

Explanation:

Given : A(2,8), B(2,1), dilated around C(6,4), dilation factor 3

To find the end points of the line segment and its length

vec(A'C) = 3 * vec(AC) or a' = 3a - 2c

a' = 3((2),(8)) - 2 ((6),(4)) = ((6),(24)) - ((12),(8)) = color(brown)(((-6),(16))

vec(B'C) = 3 * vec(BC) or b' = 3b - 2c

a' = 3((2),(1)) - 2 ((6),(4)) = ((6),(3)) - ((12),(8)) = color(brown)( ((-6),(-5))

Length of the line segment using distance formula,

vec(A'B') = sqrt((-6+6)^2 + (16+5)^2) = color(green)(21