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aliina [53]
3 years ago
5

For quadrilateral ABCD, determine the most precise name for it. A(-2,3), B(9,3), C(5,6) and D(2,6). Show your work and explain.

Mathematics
1 answer:
horsena [70]3 years ago
8 0
To solve this problem you must apply the proccedure shown below:

 1. You have the following points given in the problem above:

 A<span>(-2,3), B(9,3), C(5,6) and D(2,6)

 2. When you plot them, you obtain the figure shown in the graph attached. 

 3. Therefore, as you can see, the answer is:  the figure is a trapezoid, which is define as a quadrilateral with two parallel sides.</span>

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Find the orthogonal complement W⊥ of W and give a basis for W⊥. W = x y z : x = 1 2 t, y = − 1 2 t, z = 6t.
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Answer:

W⊥= (a, b, c)

a = v - (1/2)w

b = v

c = w

Basis for W⊥ = <(1,1,0),(-1/2,0,1)>

Step-by-step explanation:

The orthogonal complement of W is the set of vectors (a,b,c) that satisfy:

(x,y,z)·(a,b,c) = 0

ax + by + cz = 0

So, taking into account that x=12t, y=-12t and z=6t, the equation above is equal to:

12ta + -12tb + 6tc = 0

12a - 12b + 6c = 0

Then, if we made b=v and c=w and solve for a, we get:

12a - 12v + 6w = 0

a = (12v - 6w)/12

a = v - (1/2)w

Therefore, the orthogonal complement W⊥ of W has the form:

W⊥ = (a,b,c) = (v - (1/2)w, v, w)

On the other hand, we can write W⊥ as:

W⊥ = (v - (1/2)w, v, w)

W⊥ = (v,v,0) + ((-1/2)w,0,w)

W⊥ = v(1,1,0) + w(-1/2,0,1)

That means that we can write any vector of W⊥ as a linear combinations of the vectors (1,1,0) and (-1/2,0,1), so they are a basis for W⊥

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