trabeaub
Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Quadrilateral ABCD has vertices A(−2,1), B(4,4), C(5,0), and D(−1,−2).

Which side is the longest
A.BC
B.CD
C.DA
D.AB

Sagot :

VirαtKσhli

Step-by-step explanation:

Refer to the attachment ♪♪

View image VirαtKσhli
akposevictor

Using the distance formula,  [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex] to find the length of each sides, the longest side is about 6.71 units which is: d. AB

To find the longest side, we would apply the distance formula to find the length of each side.

Given:

  • A(−2,1)
  • B(4,4)
  • C(5,0)
  • D(−1,−2)

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

Length of AB:

  • Let,

[tex]A(-2,1) = (x_1, y_1)\\\\B(4,4) = (x_2, y_2)[/tex]

  • Substitute

[tex]AB = \sqrt{(4 - 1)^2 + (4 - (-2))^2}\\\\AB = \sqrt{9 + 36}\\\\AB = \sqrt{45} \\\\AB = 6.71[/tex]

Length of BC:

  • Let,

[tex]B(4,4) = (x_1, y_1)\\\\C(5,0) = (x_2, y_2)[/tex]

  • Substitute

[tex]BC= \sqrt{(0-4)^2 + (5-4)^2}\\\\BC = \sqrt{16 + 1}\\\\BC = \sqrt{17} \\\\BC =4.12[/tex]

Length of CD:

  • Let,

[tex]C(5,0) = (x_1, y_1)\\\\ D(-1,-2) = (x_2, y_2)[/tex]

  • Substitute

[tex]CD = \sqrt{(-2 - 0)^2 + (-1 - 5)^2}\\\\CD = \sqrt{4 + 36}\\\\CD = \sqrt{40} \\\\CD =6.32[/tex]

Length of DA:

  • Let,

[tex]D(-1,-2) = (x_1, y_1)\\\\ A(-2,1) = (x_2, y_2)[/tex]

  • Substitute

[tex]DA = \sqrt{(-2 - 1)^2 + (-1 - (-2))^2}\\\\DA= \sqrt{9 + 1}\\\\DA = \sqrt{10} \\\\DA = 3.16[/tex]

Therefore, the using the distance formula,  [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex] to find the length of each sides, the longest side is about 6.71 units which is: d. AB

Learn more here:

https://brainly.com/question/19799445

Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.