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Answer» First to find the area we need to find the VERTICES of the triangle.
MIDPOINT D = x1+x2 = -1........(1)
y1+y2 = 5.............................(4)
Midpoint E = x1+x3 = 14.........(2)
y1+y3 = 6...............................(5)
Midpoint F = x2+x3 = 7............(3)
y2+y3 = 7...............................(6)
Now let us find the x terms first.
(1) ........ x1 = -1-x2
Sub in (2) ........ -1-x2 + x3 = 14........(7)
Now subtracting (7) and (3)
we get, 2x3 = 22
x3 = 11
Sub x3 in (2) ........x1+11 = 14
x1 = 3
and so x2 = -4
now let us find y terms.
(3) ............y1 = 5 - y2
sub in (5).........5-y2+y3 = 6.........(8)
Now subtracting (8) and (6) we get,
y3 = 4
now sub y3 in (5)...... y1 = 2
and so
y2 = 3
now the vertices are (3,2) (-4,3) (11,4)
Area of the triangle = (3(3-4) + (-4) (4-2) + 11(2-3))/2
= (-3 -8 -11)2
= - 11
Remove the negative SIGN (-) from the number -11.
The area of the triangle is 11 sq.units.
Because the formula calls for absolute value, you SIMPLY remove the negative sign.
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