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Geometry/Geometrical Representation

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Question
Hi,

I'm stuck on a problem I was hoping you could help me with.

The problem states :

"Consider the vectors AB and CD given by the points A(0, 0), B(2, 2), C(−1, 2), and D(1, 2) in R^2. Using the geometrical representation of vector addition, draw the vector AB + CD, and give the coordinates of this vector."

According to my calculations the vector for AB has (2,2) as it's coordinates and the vector for CD (2,0). I just don't know where to go from here as I'm uncertain as to how I'm meant to find the coordinates of the vector that adding AB and CD creates.

I know how to calculate the length of vector AB and CD but that's not what's required here. Thank you in advance for any help you might be able to provide me in regards to this.

Aria

Answer
Hi Ana, I would be glad to help.  Adding vectors geometrically requires drawing a parallelogram and constructing a diagonal.  You can move vectors (as long as they same length and direction) and they will be the same unit vector.  Notice AB, goes up two and right two, so starting at C, you need to create a new vector, say CB', by going up 2 and right 2.  The coordinates of this vector are C(-1, 2) and  B' (1, 4).  You must do the same D, draw a vector going up 2 and right 2.  Call the new endpoint E, or whatever.  E(3,4).  Connect B' and E to create a parallelogram. Draw the diagonal from C to E.  this vector is your vector sum.  C (-1,2) is the start point and E (3,4) is the endpoint.  You can check the answer by adding the ordinates of AB and CD.

AB
(0,0), (2,2)

CD

(-1,2), (1,2)

AB + CD

(-1, 2), (3,4)

Because A was already at the origin there are no adjustments

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Anne Losch

Expertise

I cannot answer questions about non-Euclidean geometry (that has been a while). I can answer trigonometry, coordinate geometry, proofs, algebraic geometry, transformations, constructions, 3d shapes, area, perimeter, points, lines, planes, angles (adjacent, vertical, ...), parallel and perpendicular lines, polygons, circles, and anything taught in a geometry class.

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I have two years teaching experience in geometry; many years tutoring Geometry.

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NEA, past NCTM, MAA, AMS, and ASCD

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I have a B.S. in mathematics (and computer science), and went back for my teaching certificate (with more than enough hours for a minor in education).

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Past tutoring at Sylvan Learning Center, Huntington Learning Center, and private tutor. I have responded to questions on answers.com but would prefer to volunteer with All Experts.

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