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Mathematical Vectors Problem?
just having a little problem with working out a vectors problem. any help would be greatly appreciated thankyou :)
(a) find the area of the triangle with vertices A(-1,-3), C(4,4) and D(-5;7).
(b) Find the coordinates of the point B such that the quadrilateral ABCD is a parallelogram.
What is the area of this parallelogram?
2 Answers
- ?Lv 79 years agoFavorite Answer
(a)
Area of triangle
= (1/2) * |Ax(Cy - Dy) + Cx(Dy - Ay) + Dx(Ay - Cy)|
= (1/2) * |(-1)(4 - 7) + (4)(7 - -3) + (-5)(-3 - 4)|
= (1/2) * |3 + 40 + 35|
= (1/2) * (78)
= 39 units^2
To understand how this works, look here:
http://www.mathopenref.com/coordtrianglearea.html
(b)
C - D = (4, 4) - (-5, 7) = (4 + 5, 4 - 7) = (9, -3)
B = A + (9, -3) = (-1, -3) + (9, -3) = (9 - 1, -3 - 3) = (8, -6)
a = |DC| = (4, 4) - (-5, 7) = (9, -3)
b = |AD| = (-1, -3) - (-5, 7) = (4, -10)
Area of parallelogram
=
|i j k|
|9 -3 0|
|4 -10 0|
=
|-3 0| * i
|-10 0|
-
|9 0| * j
|4 0|
+
|9 -3| * k
|4 -10|
=
|0i + 0j - 78k|
= sqrt((-78)^2)
= 78 units^2
To understand how this method works, look here:
- 9 years ago
hey mate
just wanted to give you a heads-up
i noticed u asked some other questions of that assignment you're doing ( im a student like you doin math IM) .
you might get into trouble asking all these questions here , i suggest you delete em all after ur done coz it's kind of a plagiarism after all !! just saying this coz if i can find em all , the computer can find em all even more! in a snap.
take care
