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?

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Answer 1 · 2016-11-25T22:38:13

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

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 $A'B'=root2((-10-6)^2+(-3+19)^2)=16root2(2)$
$A'B'=4AB$

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