Answer:
Please check the explanation.
Step-by-step explanation:
Determining the length of BC
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
Determining the length of CD
Given
The distance between C(8, 10) and D(2, -2)
[tex]\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}[/tex]
[tex]CD=\sqrt{\left(2-8\right)^2+\left(-2-10\right)^2}[/tex]
[tex]=\sqrt{6^2+12^2}[/tex]
[tex]=\sqrt{36+144}[/tex]
[tex]=\sqrt{180}[/tex]
[tex]=\sqrt{36\times 5}[/tex]
[tex]=6\sqrt{5}[/tex]
Thus, the length of CD [tex]=6\sqrt{5}[/tex] units
Determining the length of ED
Given
The distance between E(-8, -4) and D(2, -2)
[tex]ED=\sqrt{\left(2-\left(-8\right)\right)^2+\left(-2-\left(-4\right)\right)^2}[/tex]
[tex]=\sqrt{10^2+2^2}[/tex]
[tex]=\sqrt{100+4}[/tex]
[tex]=\sqrt{104}[/tex]
[tex]=\sqrt{26\times \:4}[/tex]
[tex]=2\sqrt{26}[/tex]
Thus, the length of ED [tex]=2\sqrt{26}[/tex] units
Determining the length of EB
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
