SAT Question 30aa51b7: Area and Volume answer and explanation with Desmos solution

The area of a rectangle is $lw$, where $l$ and $w$ are the lengths of two adjacent sides of the rectangle. It's given that the points $(-4,-1)$, $(4,5)$, $(7,1)$, and $(-1,-5)$ form a rectangle. The points $(-4,-1)$ and $(4,5)$ form a side of the rectangle that is adjacent to the side of the rectangle formed by the points $(4,5)$ and $(7,1)$. In the xy-plane, the distance between two points, $(x_1,y_1)$ and $(x_2,y_2)$, can be found as $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$. Thus, the length, in units, of the side formed by the points $(-4,-1)$ and $(4,5)$ can be found as $\sqrt{{\left(4-(-4)\right)}^2+{\left(5-(-1)\right)}^2}$, which can be simplified to $\sqrt{100}$, or $10$. The length, in units, of the side formed by the points $(4,5)$ and $(7,1)$ can be found as $\sqrt{{\left(7-4\right)}^2+{\left(1-5\right)}^2}$, which can be simplified to $\sqrt{25}$, or $5$. Therefore, the area, in square units, of the rectangle formed by the four points shown is $(10)(5)$, or $50$.