Answer :
The question is asking for the length of figure ABCDE A is at 2, 0. B is at negative 4, 5. C is at 4, 10. D is at 8, 7. E is at 4, 5 is approximately 32.1 units.
To find the length of a figure, we need to calculate the distance between its points .
We are given the coordinates of the points A, B, C, D, and E. Let's calculate the distances between these points:
1. Distance between A and B:
Using the distance formula, we have:
[tex]AB = sqrt((x2 - x1)^2 + (y2 - y1)^2) AB = sqrt((-4 - 2)^2 + (5 - 0)^2) AB = sqrt((-6)^2 + (5)^2) AB = sqrt(36 + 25) AB = sqrt(61)[/tex]
2. Distance between B and C:
[tex]BC = sqrt((x2 - x1)^2 + (y2 - y1)^2) BC = sqrt((4 - (-4))^2 + (10 - 5)^2) BC = sqrt((8)^2 + (5)^2) BC = sqrt(64 + 25) BC = sqrt(89)[/tex]
3. Distance between C and D:
CD = sqrt[tex]((x2 - x1)^2 + (y2 - y1)^2)[/tex]
CD = sqrt[tex]((8 - 4)^2 + (7 - 10)^2)[/tex]
CD = sqrt[tex]((4)^2 + (-3)^2)[/tex]
CD = sqr[tex]t(16 + 9)[/tex]
CD = [tex]sqrt(25)[/tex]
CD = 5
4. Distance between D and E:
[tex]DE = sqrt((x2 - x1)^2 + (y2 - y1)^2) DE = sqrt((4 - 8)^2 + (5 - 7)^2) DE = sqrt((-4)^2 + (-2)^2) DE = sqrt(16 + 4) DE = sqrt(20) DE = 2sqrt(5)[/tex]
To find the length of the figure ABCDE, we sum up the distances between the points:
Length = AB + BC + CD + DE
Length = sqrt(61) + sqrt(89) + 5 + 2sqrt(5)
Now, let's calculate the length of figure ABCDE:
Length = sqrt(61) + sqrt(89) + 5 + 2sqrt(5)
[tex]Length ≈ 8.2 + 9.4 + 5 + 2(2.2)Length ≈ 17.6 + 5 + 4.4Length ≈ 27.6 + 4.4Length ≈ 32.1[/tex]
Therefore, the length of figure ABCDE is approximately 32.1 units.
To know more about figure visit:-
https://brainly.com/question/32187598
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