Question

what is the area of a rectangle with vertices (2, 3), (9, 3), (9, -2), and (2, -2)?

square units

Explanation:

Step1: Calculate the length of the rectangle

The length can be found by the difference in the \(x -\)coordinates of two adjacent vertices (since \(y -\)coordinates are the same for these two points). Using the points \((2,3)\) and \((9,3)\), the length \(l\) is \(|9 - 2|=7\).

Step2: Calculate the width of the rectangle

The width can be found by the difference in the \(y -\)coordinates of two adjacent vertices (since \(x -\)coordinates are the same for these two points). Using the points \((9,3)\) and \((9, - 2)\), the width \(w\) is \(|3-(-2)|=|3 + 2|=5\).

Step3: Calculate the area of the rectangle

The area formula of a rectangle is \(A=l\times w\). Substitute \(l = 7\) and \(w = 5\) into the formula, we get \(A=7\times5 = 35\).

Answer:

\(35\)