Given quadrilateral abcd, with vertices a (b,2c), b (4b,3c), c (5b, c), and d (2b,0), and without knowing anything about the relationship between b and c, classify the quadrilateral as precisely as possible. a) the quadrilateral is a rectangle b) the quadrilateral is a parallelogram c) a quadrilateral is a trapezoid d) the quadrilateral is a rhombus

The quadrilateral is a parallelogram

B) The quadrilateral is a parallelogram

Step-by-step explanation:

WE are given the coordinates of the quadrilateral ABCD

as A (b,2c), B (4b,3c), C (5b,c), and D (2b,0)

Let us find the slopes of all sides

Slope of AB =

From the above we know that AB and CD have same slope and hence parallel

Similarly BC and AD are parallel. Since opposite sides are parallel, ABCD is a parallelogram

To check whether rectangle, let us see slope of AB x slope of BC =-1

c/3b(2c/b) not equals -1 hence not a rectangle.

If rhombus adjacent sides should be equal

AB =

BC=

Since not equal, it is not a rhombus. ABCD is a parallelogram

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step-by-step explanation: