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)