# Yahoo Answers 05-07-14

Given M = (-1, -5) / N = (3, - 2) / P = (1, 1):
Get Q-such that MNPQ is a parallelogram. Verify that the Q obtained is actually a parallelogram. What is the perimeter?
You need a line through M parallel to PN, Slope of PN is -3/2
y+5=-3/2(x+1)
y=-3/2x-13/2
And a line through P parallel to MN. Slope of MN is 3/4
y-1=3/4(x-1)
y=3/4x+1/4
find the intersection of the two new lines:
-3/2x-13/2=3/4x+1/4
x(3/4+3/2)=-13/2-1/4
9/4x=-27/4
multiply by 4/9
x=-3
y=3/4(-3)+1/4=-9/4+1/4=-8/4=-2
Q(x,y)=(-3,-2)
verify parallel sides via slopes
Perimeter is sum of sides and since it is a parallelogram, opposite sides are equal length.
Perimeter=2(PN+MN)
PN=√2^2+3^2=√13
MN=√4^2+3^2=√25=5
Perimeter=10+2√13=approx 17.21

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