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

Guest May 8, 2019

#1**+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

CPhill May 8, 2019

#2**+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

CPhill May 8, 2019