Question

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Answer 1

Option B, 14.6 units

Explanation:

Step 1: Find the distance of AB

`AB =`
`√((x_2 - x_1)^2 + (y_2 - y_1)^2)`

`AB =`
`√((3 - 1)^2 + (5 - 3)^2)`

`AB =`
`√((2)^2 + (2)^2)`

`AB =`
`2√(2)` or 2.83...

Step 2: Find the distance of BC

`BC =`
`√((x_2 - x_1)^2 + (y_2 - y_1)^2)`

`BC = √((3 -1)^2 + (-1 - 3)^2)`

`BC = √((2)^2 + (-4)^2)`

`BC = √(4 + 16)`

`BC = √(20)`

`BC = 2√(5)` or 4.47...

Step 3: Find the perimeter

AB is the same as AD and BC is the same as DC

`2(AB) + 2(BC)`

`2(2.83) + 2(4.47)`

`5.66 + 8.94`

14.6 units

Answer: Option B, 14.6 units