Problema Solution

Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?

Answer provided by our tutors

ABCD is a parallelogram. The coordinates of D is not known. Let D(x,y).


Since in the parallelogram AB||CD, slope of AB=slope of DC.


Slope of AB=(3-4)/(1-(-2)) = 1/3


Slope of DC = (y-(-1))/(x-4) = (y+1)/(x-4)


Equating the two slopes we get:


(y+1)/(x-4) = 1/3 cross multiply


3(y + 1) = x - 4


Similarly, equating the slopes of the other two parallel sides AD and BC we get:


(y-4)/(x-(-2))=(-1-3)/(4-1)


(y-4)/(x+2) = -4/3 cross multiply


3(y-4) = (-4)(x+2)


By solving the system of equations:


3(y + 1) = x - 4


3(y - 4) = (-4)(x + 2)

........


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x = 2.2


y = -1.6


The coordinates of D are (2.2, -1.6)