Subject Test Question:

The area bound by the relationship |x|+|y|=2 is

A) 8

B) 1

C) 2

D) 4

E) there is no finite area.How do you find this algebraically?

You need to capture all the combinations of negative and positive *x* and *y*. There are four equations to consider:

*x* + *y* = 2

*–x* + *y* = 2

–*x* + (–*y*) = 2

*x* + (–*y*) = 2

Each of those is a line that can be represented in *y* = *mx* + *b* form. In the same order:

*y* = –*x* + 2

*y* = *x* + 2

*y* = –*x* – 2

*y* = *x* – 2

Those make a square with vertices at (2, 0), (0, 2), (–2, 0), and (0, –2). The diagonals of the square are 4 long, making the sides of the square long. The area of a square with those side lengths is .