Question

A quadrilateral has vertices A(3,5), B(2,0), C(7,0) and D(8,5). Which statement about the quadrilateral is true?

Answer 1

Answer:

ABCD is a rhombus with non-perpendicular adjacent sides

Step-by-step explanation:

A rhombus is a quadrilateral with four sides equal in length and non-perpendicular adjacent sides.

In the given case, when we plot the quadrilateral having vertices A(3,5), B(2,0), C(7,0) and D(8,5) then the length of each side comes out to be 5 i.e.

           AB=BC=CD=AD=5

hence given quadrilateral ABCD is a rhombus with non-perpendicular adjacent sides.

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Answer 2

Answer: ABCD is a parallelogram with non-perpendicular adjacent sides

Step-by-step explanation:

As we have two points on y=0 and two points on y=5 we can soy it has two parallel sides.

BC on y=0 has a length of 7-2=5 units

AD on y=5 has a is 8-3=5 units long

As the quadrilateral has 2 parallel sides that mesure the same, it has to be a parallelogram.

To be a rectangle the other two sides should be parallel to the y-axis, and their points should share their x coordenate. So it’s a non rectangular parallelogram.

To be a rhombus it should have 4 sides with the same lenght. AB is $\sqrt{1+5^{2} }$ that’s different to 5. Then its not a rhombus.