+5265 The vertices of square JKLM are J(-2, 4), K(-3,-1), L(2,-2), and M(3,3) Find each of the following to show that the diagonals of square JKLM are congruent perpendicular bisectors to each other.
JL=_____ KM=_____
slope of JL=_____ Slope of KM______
midpoint of JL=(_____,_____) Midpoint of KM=(______,______)
Please help me... :(
GEOMETRY IS ANNOYING, but I love math... HOW IS THAT POSSIBLE?!?!?!?!?!
+128475 JL = sqrt[ (-2-2)^2 + (-4-2)^2 ] = sqrt( 16 + 36) = sqrt(52)
KM = sqrt [ (-3-3)^2 + (-1-3)^2 ] = sqrt (36 + 16) = sqrt(52)
Slope of JL = [-2 - 4] / [2 - (-2)] = -6/4 = -3/2
Slope of KM = [3 - (-1)] / [3- (-3) ] = 4/6 = 2/3
[This proves that JL and KM are perpendicular]
J(-2, 4), K(-3,-1), L(2,-2), and M(3,3)
Midpoint of JL = [ ( -2 + 2)/2 , (-2 + 4)/2 ] = [ 0 , 1]
Midpoint of KM = [ (3 + -3)/2, (3 + -1)/2 ] = [0, 1]
So.......JL and KM have the same length, reciprocal slopes and the same mid-point.....so they are perpendicular bisectors.....
+128475 JL = sqrt[ (-2-2)^2 + (-4-2)^2 ] = sqrt( 16 + 36) = sqrt(52)
KM = sqrt [ (-3-3)^2 + (-1-3)^2 ] = sqrt (36 + 16) = sqrt(52)
Slope of JL = [-2 - 4] / [2 - (-2)] = -6/4 = -3/2
Slope of KM = [3 - (-1)] / [3- (-3) ] = 4/6 = 2/3
[This proves that JL and KM are perpendicular]
J(-2, 4), K(-3,-1), L(2,-2), and M(3,3)
Midpoint of JL = [ ( -2 + 2)/2 , (-2 + 4)/2 ] = [ 0 , 1]
Midpoint of KM = [ (3 + -3)/2, (3 + -1)/2 ] = [0, 1]
So.......JL and KM have the same length, reciprocal slopes and the same mid-point.....so they are perpendicular bisectors.....
