# Show that points A(2,3), B(8,5), C(5,3), D(2,2) are vertices of trapezoid.

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### 2 Answers

You need to find the equations of lines AB and CD and then you should check if these lines are parallel.

You should find the equation of the line AB such that:

`y - 3 = ((5-3)/(8-2))*(x-2)`

`y - 3 = (2/6)*(x - 2) `

`y - 3 = x/3 - 2/3`

You need to isolate y to the left side such that:

`y = x/3 - 2/3 + 3 `

`y = x/3 + 7/3`

You need to find the equation of the line CD such that:

`y - 3 = ((2-3)/(2-5))(x-5)`

`y - 3 = (1/3)(x - 5) =gt y = x/3 - 5/3 + 3`

`y = x/3 + 4/3`

You need to compare the slopes of lines AB and CD such that:

`m_(AB)=1/3 ; m_(CD) = 1/3`

Notice that both lines have the same slope and different y intercepts, hence the line AB is parallel to CD.

**Hence, the points `A,B,C,D` express the vertices of trapezoid `ABCD.` **

You have to show that two lines are parallel and the other two aren't.

To show that they are parallel, you have to find the slope of the line using the slope formula.

And the other two lines, you have to show that they are not parallel by using the slope formula again.