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sleet_krkn [62]
2 years ago
6

What is the most precise name for quadrilateral ABCD with vertices A(-3,1) , B(-1,4) , C(5,4) , and D(3,1)?

Mathematics
2 answers:
Natasha2012 [34]2 years ago
4 0
The best and most correct answer among the choices provided by your question is the fourth choice or letter D.

We can imply from the given points that the figure is four-side or a quadrilateral.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
hram777 [196]2 years ago
4 0

Answer:

ABCD is a parallelogram.

Step-by-step explanation:

Given quadrilateral ABCD with vertices A(-3,1), B(-1,4), C(5,4) and D(3,1)

we have to give the most precise name for quadrilateral ABCD.

Using distance formula

Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

AB=\sqrt{(-1+3)^2+(4-1)^2}=\sqrt{4+9}=\sqrt{13}units

BC=\sqrt{(5+1)^2+(4-4)^2}=\sqrt{36}=\sqrt{6}units

CD=\sqrt{(3-5)^2+(1-4)^2}=\sqrt{4+9}=\sqrt{13}units

DA=\sqrt{(-3-3)^2+(1-1)^2}=\sqrt{36}=\sqrt{6}units

Opposite sides of quadrilateral ABCD are equal.

Now, we find the slope of the sides of quadrilateral

\text{Slope of AB=}\frac{y_2-y_1}{x_2-x_1}=\frac{4-1}{-1+3}=\frac{3}{2}

\text{Slope of BC=}\frac{y_2-y_1}{x_2-x_1}=\frac{4-4}{5+1}=0

\text{Slope of CD=}\frac{y_2-y_1}{x_2-x_1}=\frac{1-4}{3-5}=\frac{3}{2}

\text{Slope of DA=}\frac{y_2-y_1}{x_2-x_1}=\frac{1-1}{-3-3}=0

Slopes of opposite sides are equal.

⇒ The sides of opposite sides of quadrilateral are parallel and equal.

⇒ ABCD is a parallelogram.

Option b) is correct.

 

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