1. **Problem Statement:** Find the coordinates of points B and D on the computer screen window, and calculate distances from A to C and B to D given pixel size. Also, identify which icon was clicked at coordinates (410, 670). Finally, write and use the distance formula for two points. 2. **Given:** - A = (1000, 200) (bottom-left corner) - C = (900, 800) (upper-right corner) - B = (x_B, y_B) (bottom-right corner) - D = (x_D, y_D) (upper-left corner) - Pixel size = 0.25 mm square 3. **Step 1: Find coordinates of B and D.** - Since A and B share the same y-coordinate (bottom edge), and B and C share the same x-coordinate (right edge): $$y_B = y_A = 200$$ $$x_B = x_C = 900$$ So, $$B = (900, 200)$$ - Since A and D share the same x-coordinate (left edge), and D and C share the same y-coordinate (top edge): $$x_D = x_A = 1000$$ $$y_D = y_C = 800$$ So, $$D = (1000, 800)$$ 4. **Step 2: Calculate distance from A to C.** - Use the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ - Substitute points A(1000, 200) and C(900, 800): $$d = \sqrt{(900 - 1000)^2 + (800 - 200)^2} = \sqrt{(-100)^2 + 600^2} = \sqrt{10000 + 360000} = \sqrt{370000}$$ - Distance in pixels: $$\sqrt{370000}$$ pixels - Convert to mm: $$\sqrt{370000} \times 0.25 = 0.25 \times \sqrt{370000}$$ mm 5. **Step 3: Calculate distance from B to D.** - Points B(900, 200) and D(1000, 800): $$d = \sqrt{(1000 - 900)^2 + (800 - 200)^2} = \sqrt{100^2 + 600^2} = \sqrt{10000 + 360000} = \sqrt{370000}$$ - Distance in pixels: $$\sqrt{370000}$$ pixels - Convert to mm: $$0.25 \times \sqrt{370000}$$ mm 6. **Step 4: Identify clicked icon at (410, 670).** - The problem does not provide icon coordinates, so we cannot determine which icon was clicked based on given data. 7. **Step 5: Write the distance formula for two points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$.** $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 8. **Step 6: Use the formula to find the distance between opposite corners of the square with corners (4,4) and (1,1).** $$d = \sqrt{(4 - 1)^2 + (4 - 1)^2} = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} = 3\sqrt{2}$$ **Final answers:** - B = (900, 200) - D = (1000, 800) - Distance A to C = $$0.25 \times \sqrt{370000}$$ mm - Distance B to D = $$0.25 \times \sqrt{370000}$$ mm - Distance between square corners = $$3\sqrt{2}$$ - Icon clicked at (410, 670): Cannot determine with given data.