Answer:
Please check the explanation.
Step-by-step explanation:
<u>Determining the length of BC</u>
From the diagram, it is clear that
- The point B is located at (-8, 10) and point C is located at (8, 10)
Since points A and C are located on a horizontal straight line. Thus, the length of BC can be determined by counting the x-axis units from reaching x = -8 to x = 8. i.e. 8-(-8) = 8+8 = 16
Thus, the length of BC = 16 units
<u>Determining the length of CD</u>
Given
The distance between C(8, 10) and D(2, -2)
![\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}](https://tex.z-dn.net/?f=%5Cmathrm%7BCompute%5C%3Athe%5C%3Adistance%5C%3Abetween%5C%3A%7D%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3A%5Cquad%20%5Csqrt%7B%5Cleft%28x_2-x_1%5Cright%29%5E2%2B%5Cleft%28y_2-y_1%5Cright%29%5E2%7D)
![CD=\sqrt{\left(2-8\right)^2+\left(-2-10\right)^2}](https://tex.z-dn.net/?f=CD%3D%5Csqrt%7B%5Cleft%282-8%5Cright%29%5E2%2B%5Cleft%28-2-10%5Cright%29%5E2%7D)
![=\sqrt{6^2+12^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B6%5E2%2B12%5E2%7D)
![=\sqrt{36+144}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B36%2B144%7D)
![=\sqrt{180}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B180%7D)
![=\sqrt{36\times 5}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B36%5Ctimes%205%7D)
![=6\sqrt{5}](https://tex.z-dn.net/?f=%3D6%5Csqrt%7B5%7D)
Thus, the length of CD
units
<u>Determining the length of ED</u>
Given
The distance between E(-8, -4) and D(2, -2)
![ED=\sqrt{\left(2-\left(-8\right)\right)^2+\left(-2-\left(-4\right)\right)^2}](https://tex.z-dn.net/?f=ED%3D%5Csqrt%7B%5Cleft%282-%5Cleft%28-8%5Cright%29%5Cright%29%5E2%2B%5Cleft%28-2-%5Cleft%28-4%5Cright%29%5Cright%29%5E2%7D)
![=\sqrt{10^2+2^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B10%5E2%2B2%5E2%7D)
![=\sqrt{100+4}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B100%2B4%7D)
![=\sqrt{104}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B104%7D)
![=\sqrt{26\times \:4}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B26%5Ctimes%20%5C%3A4%7D)
![=2\sqrt{26}](https://tex.z-dn.net/?f=%3D2%5Csqrt%7B26%7D)
Thus, the length of ED
units
<u>Determining the length of EB</u>
From the diagram, it is clear that
- The point E is located at (-8, -4) and the point B is located at (-8, 10)
Since points E and B are located on a vertical straight line. Thus, the length of EB can be determined by counting the y-axis units from reaching y = -4 to y = 10. i.e. 10-(-4) = 10+4 = 14
Thus, the length of EB = 14 units