SOLUTION: A triangle has the vertices of A(1, 18), D( - 7, 4), and C(5, 0). B and E are the midpoints of AC and AD respectively. a) Provide a labelled diagram for the triangle and lin

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A triangle has the vertices of A(1, 18), D( - 7, 4), and C(5, 0). B and E are the midpoints of AC and AD respectively. a) Provide a labelled diagram for the triangle and lin      Log On


   

Question 1180246: A triangle has the vertices of A(1, 18), D( - 7, 4), and C(5, 0). B and E are the midpoints of AC and AD respectively.
a) Provide a labelled diagram for the triangle and lines above (2M).
b) Using analytical geometry calculations, determine if the line segments BE and CD are parallel (show all formulas and work)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

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Calculate mid point of AB and AC
x=(-1+7)/2 =-3
y= (18+4)/2 =11
slope of EF
x1 y1 x2 y2
-3 11 3 9

slope m = (y2-y1)/(x2-x1)
( 9 - 11 )/( 3 - -3 )
( -2 / 6 )
m= -0.33

slope of BC
x1 y1 x2 y2
-7 4 5 0

slope m = (y2-y1)/(x2-x1)
( 0 - 4 )/( 5 - -7 )
( -4 / 12 )
m= -0.33
slope EF equal to slope BC
so EF parallel to BC