Question

you are designing a top - down view of a rectangular fish tank. the corners of the tank on the coordinate plane are: a(1,2), b(7,2), c(7,6), and d(1,6). use the coordinate plane to find the area of the fish tank, a = l·w ; a 24 units² b 16 units² c 20 units² d 12 units²

Explanation:

Step1: Find the length

For a rectangle with vertices \(A(1,2)\), \(B(7,2)\), \(C(7,6)\), and \(D(1,6)\), the length \(L\) can be found using the \(x -\)coordinates of two points on the same horizontal line. Using points \(A(1,2)\) and \(B(7,2)\), \(L=\vert7 - 1\vert=6\).

Step2: Find the width

Using the \(y -\)coordinates of two points on the same vertical line, say \(B(7,2)\) and \(C(7,6)\), \(W=\vert6 - 2\vert = 4\).

Step3: Calculate the area

Using the formula \(A = L\times W\), we substitute \(L = 6\) and \(W=4\), so \(A=6\times4 = 24\).

Answer:

A. 24 units²