Given :
Four points A(2,9) , B(7,9) , C(-3,-5) and D(-3,1) .
To Find :
Are AB and CD congruent .
Solution :
Two line segment are congruent when their length is equal .
Now , length of line segment with points (a,b) and (c,d) .
[tex]L=\sqrt{(a-c)^2+(b-d)^2}[/tex] .
So , length of AB is :
[tex]AB=\sqrt{(2-7)^2+(9-9)^2}\\\\AB=\sqrt{(-5)^2+0^2}\\\\AB=5\ units[/tex]
Also , length of CD is :
[tex]CD=\sqrt{(-3-(-3))^2+(-5-1)^2}\\\\CD=\sqrt{0^2+(-6)^2}\\\\AB=6\ units[/tex]
Since , length of AB and CD is not equal .
Therefore , the line segment AB and CD are not congruent .
