Vectors question - given points

In summary, the conversation is about a person who forgot their textbook and is asking for help with a geometry problem involving points A(-3,1), B(4,7), C(9,2), and D(2,-4). They need to prove that these points form a parallelogram by showing that the opposite sides are parallel and equal in length. They are instructed to form vectors of AB, DC, AD, and BC, with the first two and last two being parallel.
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Vectors question -- given points

Lads, You're going to laugh at me, but I started my new unit today, and I forgot my dang textbook at school, I'm doing as much research online as I can, but I'm having a rough time figuring this guy out. Any insight would be very helpful! Thanks!

Homework Statement



Given the points A(-3,1), B(4,7), C(9,2), and D(2,-4) prove algebraically that they form a parallelogram.
 
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  • #2


If these points form a parallelogram, opposite sides must be parallel and equal in length. Form vectors of AB, DC, AD, and BC. The first two vectors I've listed should be equal (and therefore parallel). So should the last two.
 

FAQ: Vectors question - given points

1. What is a vector?

A vector is a mathematical object that has both magnitude and direction. It is represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude.

2. How do you calculate the magnitude of a vector?

The magnitude of a vector can be calculated using the Pythagorean theorem, by taking the square root of the sum of the squared components of the vector. Alternatively, you can use the magnitude formula, which is the square root of the dot product of the vector with itself.

3. What are the coordinates of a vector?

The coordinates of a vector represent the components of the vector in a specific coordinate system. For example, in a two-dimensional coordinate system, a vector may have x and y coordinates, while in a three-dimensional coordinate system, it may have x, y, and z coordinates.

4. How do you add two vectors?

To add two vectors, you simply add the corresponding components of the vectors. For example, if you have two vectors, (2,3) and (4,1), the sum of the two vectors would be (2+4, 3+1), which is (6,4).

5. How can vectors be used in real life?

Vectors have many applications in real life, including in physics, engineering, and computer graphics. They can be used to represent forces, velocities, and movements, and are also used in navigation systems, video games, and simulations.

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