Find the area of the rectangle that has the following ordered pairs: F(-3,1) G(-1,0) H(-2,-4), J(-5,-2)?

To find the area of a rectangle given the coordinates of its vertices, you need to calculate the lengths of its sides and then multiply the length of one side by the length of an adjacent side.

In the given case, the vertices are labeled as F(-3,1), G(-1,0), H(-2,-4), and J(-5,-2).

To calculate the lengths of the sides, we can use the distance formula. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Let's calculate the lengths of the sides FG, GH, HJ, and FJ:

FG = √((-1 - (-3))^2 + (0 - 1)^2) = √(2^2 + (-1)^2) = √(4 + 1) = √5
GH = √((-2 - (-1))^2 + (-4 - 0)^2) = √(1^2 + (-4)^2) = √(1 + 16) = √17
HJ = √((-5 - (-2))^2 + (-2 - (-4))^2) = √(3^2 + 2^2) = √(9 + 4) = √13
FJ = √((-5 - (-3))^2 + (-2 - 1)^2) = √(2^2 + (-3)^2) = √(4 + 9) = √13

Now that we have the lengths of two adjacent sides, FG and GH, we can multiply them to find the area.

Area = FG * GH = √5 * √17 = √(5 * 17) = √85

Therefore, the area of the rectangle is √85 square units.