Question

Find the perimeter, in units, of quadrilateral ABCD with vertices A = (1,1), B = (4,4), C = (7,1), D = (4,-2).

Answer 1

`12√(2)`

Explanation:

The easiest way personally for me is to graph it out, but you can also calculate it out.

A = (1,1)

B = (4,4)

C = (7,1)

D = (4,-2)

Attached is the distance formula. Use it to your advantage. Find the slope for all the points:

Point A to B:
`\sqrt{(4-1)^(2)+(4-1)^(2) }` =
`√(9+9 )`

Point B to C:
`\sqrt{(7-4)^(2)+(1-4)^(2) }` =
`√(9+9)`

Point C to D:
`\sqrt{(4-7)^(2)+(-2-1)^(2) }` =
`√(9+9)`

Point D to A:
`\sqrt{(4-1)^(2)+(-2-1)^(2) }` =
`√(9+9)`

When you add all of it up, it will equal to
`√(18) + √(18) + √(18) + √(18) = 4\sqrt{18` and which simplifies to
`12√(2)`.