Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

a quadrilateral has vertices A(4,5), B(2,4), C(4,3), and D(6,4) which statement about the quadrilateral is true A ABCD is a parallelogram with noncongruent adj sides B ABCD is a trapezoid with only one pair of parallel sides C ABCD is a rectangle with noncongruent adj sides D ABCD is a square E ABCD is a rhombus with non perpendicular adj sides

Sagot :

lulu1991
The answer is E. If you draw the quadrilateral out, you can clearly see what it looks like. And you can know from the coordinates that the diagonal of this quadrilateral is not equal. So it can not be rectangle. And also AB//CD and AD//BC.
frika

Let's find the lengths of all sides:

[tex] AB=\sqrt{(4-2)^2+(5-4)^2}=\sqrt{4+1} =\sqrt{5} ,\\ BC=\sqrt{(2-4)^2+(4-3)^2}=\sqrt{4+1} =\sqrt{5},\\ CD=\sqrt{(4-6)^2+(3-4)^2} =\sqrt{4+1} =\sqrt{5},\\ AD=\sqrt{(6-4)^2+(4-5)^2}=\sqrt{4+1} =\sqrt{5} [/tex].

All sides are congruent, then this quadrilateral may occur to be square or rhombus. Check whether sides AB and AD are perpendicular. With this aim you should find vectors [tex] \vec{AB} [/tex] and [tex] \vec{AD} [/tex]:

[tex] \vec{AB}=(2-4,4-5) =(-2,-1)[/tex] ,

[tex] \vec{AD}=(6-4,4-5) =(2,-1)[/tex] .

The dot product: [tex] \vec{AB}\cdot \vec{AD}=-2\cdot 2+(-1)\cdot (-1)=-4+1=-3\neq 0 [/tex]. This means that sides AB and AD are not perpendicular and quarilateral ABCD is not square.

Answer: correct choice is E.

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.