# A line segment has endpoints at (4 ,7 ) and (2 ,5 ). The line segment is dilated by a factor of 4  around (3 ,3 ). What are the new endpoints and length of the line segment?

Nov 28, 2016

$\text{the new end points are:} A ' \left(7 , 19\right) , B ' \left(- 1 , 11\right)$

$\text{length of the new line segment is :} 8 \sqrt{2}$

#### Explanation:

$\text{1- draw Point objects A(4,7),B(2,5),D(3,3) and line segment}$

$\text{2-find the new location of the Point B}$

$x = 3 - 1 \cdot 4 = 3 - 4 = - 1$

$y = 3 + 2 \cdot 4 = 3 + 8 = 11$

$\text{the new location of B is } B ' \left(- 1 , 11\right)$

$\text{3-find the new location of A}$

$x = 3 + 1 \cdot 4 = 3 + 4 = 7$

$y = 3 + 4 \cdot 4 = 3 + 16 = 19$

$A ' \left(7 , 19\right)$

$\text{4-draw the new line segment } A ' \left(7 , 19\right) , B ' \left(- 1 , 11\right)$

$\text{length of the new line segment :}$

$A ' B ' = \sqrt{{\left(19 - 11\right)}^{2} + {\left(7 + 1\right)}^{2}}$

$A ' B ' = \sqrt{{8}^{2} + {8}^{2}}$

$A ' B ' = \sqrt{64 + 64}$

$A ' B ' = 8 \sqrt{2}$