Question

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Answer 1

Please check the explanation.

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

• C (8, 10)

• D (2, -2)

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 √(\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2)`

`CD=√(\left(2-8\right)^2+\left(-2-10\right)^2)`

`=√(6^2+12^2)`

`=√(36+144)`

`=√(180)`

`=√(36* 5)`

`=6√(5)`

Thus, the length of CD
`=6√(5)` units

Determining the length of ED

Given

• E (-8, -4)

• D (2, -2)

The distance between E(-8, -4) and D(2, -2)

`ED=√(\left(2-\left(-8\right)\right)^2+\left(-2-\left(-4\right)\right)^2)`

`=√(10^2+2^2)`

`=√(100+4)`

`=√(104)`

`=√(26* \:4)`

`=2√(26)`

Thus, the length of ED
`=2√(26)` 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