SOLUTION: A triangle has vertices A(3,4), B(-2,0), and C(5,0). Find the midpoint of each side, and label these midpoints D, E, and F. Verify that the area of triangle ABC is four times th

Algebra ->  Length-and-distance -> SOLUTION: A triangle has vertices A(3,4), B(-2,0), and C(5,0). Find the midpoint of each side, and label these midpoints D, E, and F. Verify that the area of triangle ABC is four times th      Log On


   

Question 1161458: A triangle has vertices A(3,4), B(-2,0), and C(5,0). Find the midpoint of each side, and label these midpoints D, E, and F.
Verify that the area of triangle ABC is four times the area of triangle DEF
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


D(0.5,2); E(1.5,0); F(4,2)

Area of ABC: one-half base times height = %281%2F2%29%287%29%284%29+=+14

Area of DEF: one-half base times height = %281%2F2%29%283.5%29%282%29+=+3.5

14/3.4 = 4

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A triangle has vertices A(3,4), B(-2,0), and C(5,0).
Find the midpoint of each side, and label these midpoints D,+E, and F.
the midpoint of A(3,4) and+B(-2,0) is D(%283-2%29%2F2,%284%2B0%29%2F2)->D(1%2F2,2)
the midpoint of A(3,4) and C(5,0) is E(4,2)
the midpoint of B(-2,0) and C(5,0) is F(3%2F2,0)




that the area of triangle ABC is:
A=%28b%2Ah%29%2F2
b= distance between A and C which is 7 units
h= shortest distance between x-axis and B+which is 4 units
A=%287%2A4%29%2F2
A=7%2A2
A=14+square units
the area of triangle DEF is:
base is DE ->b=+4-1%2F2=7%2F2
h=2
A=%28%287%2F2%29%2A2%29%2F2
A=7%2F2
A=3.5
Verify that the area of triangle ABC is four times the area of triangle DEF:
14=4%2A3.5
14=14-> verified