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