Question

1. a rectangle in the coordinate plane has vertices f(0, 5) and i(12, -4). find the area if fg is 4.

Explanation:

Step1: Calculate length of FI

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $F(0,5)$ and $I(12,-4)$, we have $x_1 = 0,y_1 = 5,x_2=12,y_2=-4$. Then $FI=\sqrt{(12 - 0)^2+(-4 - 5)^2}=\sqrt{12^2+(-9)^2}=\sqrt{144 + 81}=\sqrt{225}=15$.

Step2: Determine the other - side length of the rectangle

In a rectangle, if one side is $FG = 4$ and the diagonal (or another side - related length) is $FI = 15$, and since the area of a rectangle $A=FG\times FI$ (assuming $FG$ and $FI$ are adjacent - side lengths of the rectangle, which is valid as we are using the given information to find the area).

Answer:

$60$