Question

A line segment has endpoints at `(1 ,6 )` and `(5 ,2 )`. The line segment is dilated by a factor of `4` around `(2 ,1 )`. What are the new endpoints and length of the line segment?

Answer 1

`A'(6,-19)` and `B'(-10;-3)`

Explanation:

We have to solve the dilation equation of factor 4 for x and y

`x_C=(4*x_A+x_A')/5` and `y_C=(4*y_A+y_A')/5`

with `C(2;1)` and `A(1;6)` we have
`2=(4*1+x_A')/5` from which it is `x_A'=6`

and `1=(4*6+y_A')/5` from which it is `y_B'=-19`

the same for `B'`
`2=(4*5+x_B')/5` from which it is `x_B'=-10`
`1=(4*2+y_B')/5` from which it is `y_B'=-3`

It is enough to check that `AB=root2((5-1)^2+(2-6)^2)=4root2(2)`
and `A'B'=root2((-10-6)^2+(-3+19)^2)=16root2(2)`
`A'B'=4AB`