Geometry: What type of quadrilateral has vertices at....

[josh90]

What type of quadrilateral has vertices at (0,0), (a,b), (c,b), and (c+a,0)?

I am confused on how to set this up on the coordinate plane. Can someone please show me how to do it? Thank you.

 

[pka]

Please review what you have posted.
Are there some additional conditions on a, b and c?
For example, are they all positive? Is a<b<c?
Without more conditions they are multiple answers to the question.

 

[soroban]

Hello, josh90!

What type of quadrilateral has vertices at (0,0), (a,b), (c,b), and (c+a,0)?

        |   (a,b)       (c,b)
       b+     * - - - - - *
        |    /             \
        |   /               \
        |  /                 \
        | /                   \
        |/                     \
    - - * - - + - - - - - + - - * - -
      (0,0)   a           c   (c+a,0)

Looks like an isosceles trapezoid to me . . .

In desperation, you could have stuck in some numbers yourself
$\displaystyle \;\;\;$like: $\displaystyle \,a\,=\,2,\;b\,=\,3\;c\,=\,5$
Then plot: $\displaystyle \,(0,0),\;(2,3),\;(5,3),\;(7,0)$

 

[pka]

Looks like an isosceles trapezoid to me . . .
In desperation, you could have stuck in some numbers yourself
$\displaystyle \;\;\;$like: $\displaystyle \,a\,=\,2,\;b\,=\,3\;c\,=\,5$
Then plot: $\displaystyle \,(0,0),\;(2,3),\;(5,3),\;(7,0)$[/size]

What if a=-2, b=1, and c=2?

What if a=6, b=1, and c=2?

 

[josh90]

Looks like an isosceles trapezoid to me . . .
In desperation, you could have stuck in some numbers yourself
$\displaystyle \;\;\;$like: $\displaystyle \,a\,=\,2,\;b\,=\,3\;c\,=\,5$
Then plot: $\displaystyle \,(0,0),\;(2,3),\;(5,3),\;(7,0)$[/size]

What if a=-2, b=1, and c=2?

What if a=6, b=1, and c=2?

pka, that was all I was given, there was nothing in the question that told me whether a was less than B or so on.

 

[pka]

pka, that was all I was given, there was nothing in the question that told me whether a was less than B or so on.

Despite the other response, absent further information there are multiple answers.
If a=-2, b=1, & c= 2 then the figure is a triangle.
If a=4, b=1, & c=2 then we get two triangles meeting at a common vertex.
If 0<a<c & b=1 the as was suggested we get an isosceles trapezoid.

I will say that when I teach abstract geometry, I do give such questions.
That is, a question that has multiple answers.
Such a question separates the sheep from the goats.
You can see this in the responses to this question.