# A line segment has endpoints at (7 ,6 ) and (9 ,2 ). The line segment is dilated by a factor of 4  around (4 ,3 ). What are the new endpoints and length of the line segment?

Nov 16, 2016

$\text{please have a look the animation below}$

$\text{The new end points of line segment are :} F \left(16 , 15\right) , I \left(24 , - 1\right)$

$\text{Length of the line segment is :} 17.89$

#### Explanation:

$\text{the coordinates of point F:}$

$C J \cdot \text{factor} = 3 \cdot 4 = 12$

$4 + 12 = 16 \text{ the x coordinate of F}$

$A J \cdot \text{factor} = 3 \cdot 4 = 12$

$3 + 12 = 15 \text{the y coordinate of F}$

$F \left(16 , 15\right)$

$\text{the coordinates of I Point:}$

$Z B \cdot \text{factor} = 5 \cdot 4 = 20$

$4 + 20 = 24 \text{ the x coordinate of I}$

$C Z \cdot \text{factor} = 1 \cdot 4 = 4$

3-4=-1" the y coordinate of I")

$I = \left(24 , - 1\right)$

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

FI=sqrt((16-24)^2+(15+1)^2)

$F I = \sqrt{64 + 256}$

$F I = \sqrt{320}$

$F I = 17.89$