In the cartesian coordinate system, three points A(0,0), B(6,0), and C(0,4) are given. What is the area of the rectangle formed by these three points?
Answer
Step 3: The area of a rectangle is given by the product of its length and breadth. So, the area of the rectangle formed by points A, B and C is \(AB \times AC = 6 \times 4 = 24\) square units.
Step 1 ：Step 1: Identify the three points which form a right triangle with one side on the x-axis and the other on the y-axis. These sides will be the sides of our rectangle. In this case, AB and AC are the sides of the rectangle.
Step 2 ：Step 2: Use the distance formula to calculate the lengths of AB and AC. \(AB = \sqrt{(6-0)^2+(0-0)^2} = 6\) and \(AC = \sqrt{(0-0)^2+(4-0)^2} = 4\)
Step 3 ：Step 3: The area of a rectangle is given by the product of its length and breadth. So, the area of the rectangle formed by points A, B and C is \(AB \times AC = 6 \times 4 = 24\) square units.
