This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Determine the dimensions of the first rectangle. The top-left corner of the first rectangle is (5, 9). The top-right corner of the first rectangle is (12, 9). The width of the rectangle is the difference in x-coordinates: Width = 12 - 5 = 7 The point (12, 3) is given, which is the bottom-right corner of the first rectangle. The height of the rectangle is the difference in y-coordinates: Height = 9 - 3 = 6 Step 2: Determine the coordinates of point A. Point A is the bottom-right corner of the first rectangle. From the given information, this point is (12, 3). A = (12, 3) Step 3: Determine the coordinates of point B. The problem states that the two rectangles are identical. This means the second rectangle also has a width of 7 units and a height of 6 units. Point A (12, 3) is the top-left corner of the second rectangle. To find the coordinates of point B, which is the bottom-right corner of the second rectangle: The x-coordinate of B will be the x-coordinate of A plus the width: x_B = 12 + 7 = 19 The y-coordinate of B will be the y-coordinate of A minus the height (since the rectangle extends downwards from A): y_B = 3 - 6 = -3 So, the coordinates of point B are (19, -3). B = (19, -3) The coordinates are: A is (12, 3) B is (19, -3) For the second part of the question: n stands for a whole number. n is greater than 30, which means n > 30. n is less than 100, which means n < 100. Combining these conditions, we have 30 < n < 100. Since n is a whole number (non-negative integer), the possible values for n are integers strictly between 30 and 100. The numbers that n stands for are 31, 32, 33, , 99.