SOLUTION: find cd and ef then determine if cd is congruent to ef d is (-2,4) c is (-5,0) e is (2,2) f is (5,-2

Algebra ->  Length-and-distance -> SOLUTION: find cd and ef then determine if cd is congruent to ef d is (-2,4) c is (-5,0) e is (2,2) f is (5,-2      Log On


   

Question 356942: find cd and ef then determine if cd is congruent to ef
d is (-2,4)
c is (-5,0)
e is (2,2)
f is (5,-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, we need to find the length of cd. So we need to find the distance between (-5,0) and (-2,4).


Note: is the first point . So this means that x%5B1%5D=-5 and y%5B1%5D=0.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=4.


d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%28-5--2%29%5E2%2B%280-4%29%5E2%29 Plug in x%5B1%5D=-5, x%5B2%5D=-2, y%5B1%5D=0, and y%5B2%5D=4.


d=sqrt%28%28-3%29%5E2%2B%280-4%29%5E2%29 Subtract -2 from -5 to get -3.


d=sqrt%28%28-3%29%5E2%2B%28-4%29%5E2%29 Subtract 4 from 0 to get -4.


d=sqrt%289%2B%28-4%29%5E2%29 Square -3 to get 9.


d=sqrt%289%2B16%29 Square -4 to get 16.


d=sqrt%2825%29 Add 9 to 16 to get 25.


d=5 Take the square root of 25 to get 5.


So our answer is d=5


So the distance between the two points is 5 units.


So the length of cd is 5 units.


-------------------------------------

Now we need to find the length of ef. So we need to find the distance between the points (2,2) and (5,-2)


Note: is the first point . So this means that x%5B1%5D=2 and y%5B1%5D=2.
Also, is the second point . So this means that x%5B2%5D=5 and y%5B2%5D=-2.


d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%282-5%29%5E2%2B%282--2%29%5E2%29 Plug in x%5B1%5D=2, x%5B2%5D=5, y%5B1%5D=2, and y%5B2%5D=-2.


d=sqrt%28%28-3%29%5E2%2B%282--2%29%5E2%29 Subtract 5 from 2 to get -3.


d=sqrt%28%28-3%29%5E2%2B%284%29%5E2%29 Subtract -2 from 2 to get 4.


d=sqrt%289%2B%284%29%5E2%29 Square -3 to get 9.


d=sqrt%289%2B16%29 Square 4 to get 16.


d=sqrt%2825%29 Add 9 to 16 to get 25.


d=5 Take the square root of 25 to get 5.


So our answer is d=5


So the distance between the two points is also 5 units.


So the length of ef is also 5 units.


This means that cd and ef are congruent (since they are the same length).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim