Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

After exploring the properties of quadrilaterals, Jackie concluded that quadrilateral ABCD formed by vertices A(2, 1), B(5, -1), C(3, -4), and D(0, -2) is a square.
Part A
Determine the slope of each side of the quadrilateral. What do the slopes indicate about the sides of the quadrilateral? Show your work.
Part B
Determine the length of each side of the quadrilateral. What do the lengths indicate about the sides of the quadrilateral? Show your work.
Part C
Was Jackie's conclusion correct? Explain your reasoning.

Sagot :

MrRoyal

Jackie's conclusion about the quadrilateral is correct because the slopes are opposite reciprocals, and the side lengths are congruent

The slope of each side

The vertices are given as:

A(2, 1), B(5, -1), C(3, -4), and D(0, -2)

The slope is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

So, we have

[tex]AB = \frac{-1 -1}{5-2}[/tex]

[tex]AB = -\frac{2}{3}[/tex]

[tex]BC = \frac{-4 + 1}{3 -5}[/tex]

[tex]BC = \frac{3}{2}[/tex]

[tex]CD = \frac{-2 +4}{0-3}[/tex]

[tex]CD = -\frac{2}{3}[/tex]

[tex]DA = \frac{1 + 2}{2 - 0}[/tex]

[tex]DA = \frac{3}{2}[/tex]

The slope shows that the adjacent sides of the quadrilaterals are perpendicular to one another because the slopes are opposite reciprocals

The distance of each side

The distance is calculated as:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(2 - 5)^2 + (1 + 1)^2}[/tex]

[tex]AB = \sqrt{13}[/tex]

[tex]BC = \sqrt{(5 - 3)^2 + (-1 + 4)^2}[/tex]

[tex]BC = \sqrt{13}[/tex]

[tex]CD = \sqrt{(3 - 0)^2 + (-4 + 2)^2}[/tex]

[tex]CD = \sqrt{13}[/tex]


[tex]DA = \sqrt{(0 - 2)^2 + (-2 -1)^2}[/tex]

[tex]DA = \sqrt{13}[/tex]

The lengths indicate that the side lengths of the quadrilaterals are congruent

The conclusion

Because the slopes are opposite reciprocals, and the side lengths are equal; then we can conclude that Jackie's conclusion is correct

Read more about quadrilaterals at:

https://brainly.com/question/16691874

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.