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Please help and show work. I've been stuck on these. I really need to understand how to do these. Thanks. 

 May 8, 2019
 #1
avatar+111455 
+1

If UT is a perpendicular bisector of NW....T must be the midpoint of  NW

So....the midpoint of NW  =

 

[ (-4 + 2) / 2 , ( 3 + 5) / 2 ]  =   (-2/2 , 8/2) = (-1, 4)  = T

 

Check this.....slope of NW  =   [ 5 - 3] / [ 2 - - 4 ]  =  2 / 6  =  1/3

 

Slope of  UT  =  [ 1 - 4 ]/  [ 0, -  -1]   =  -3/1  =  -3

 

Since NW and UT have negative reciprocal slopes....they are also perpendicular

 

 

cool cool cool

 May 8, 2019
 #2
avatar+111455 
+1

Second  one.....we have the points  (-2, - 2)    (-1, 3) (2, 2)

 

Distance between   (-2, -2)  and (-1, 3)  =  sqrt [ ( -2 - - 1)^2 + (-2 - 3)^2 ] = sqrt [ (-1)^2 + (-5)^2 ] =

sqrt [ 1 + 25]  =  sqrt (26)

 

Distance between (-2, -2)  and (2, 2)  = sqrt [ ( -2 - 2)^2 + (-2 - 2)^2 ]  = sqrt [ (-4)^2 + (-4)^2 ] =

sqrt [ 16 + 16 ]  =  sqrt (32)  =  4sqrt(2)

 

Distance between  (-1,3)  and (2, 2)  = sqrt [ ( -1 - 2)^2 + ( 3 - 2)^2 ]  = sqrt [ (-3)^2 + (1)^2 ]  =

sqrt [ 9 + 1 ]  =  sqrt(10)

 

So.....the perimeter  =     sqrt (26) + 4sqrt(2) + sqrt(10) ≈  13.92 units

 

 

cool cool cool

 May 8, 2019
 #3
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+1

Thank you so much for your help! I truly appreciate it!!

Guest May 8, 2019

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