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
Here's the solution for question 6. a) The vertices of ABCD are given as A(2, 8), B(2, 4), C(8, 4), and D(8, 8). To draw ABCD, plot these points on a graph sheet with perpendicular axes Ox and Oy, using a scale of 2 cm to 2 units (which means 1 cm represents 1 unit) for intervals -10 x 10 and -10 y 10. Then connect the points A to B, B to C, C to D, and D to A. b) To find the image A_1B_1C_1D_1 of ABCD under a reflection in the y-axis, we use the transformation rule (x, y) (-x, y). Step 1: Apply the rule to point A(2, 8). A_1 = (-2, 8) Step 2: Apply the rule to point B(2, 4). B_1 = (-2, 4) Step 3: Apply the rule to point C(8, 4). C_1 = (-8, 4) Step 4: Apply the rule to point D(8, 8). D_1 = (-8, 8) The vertices of A_1B_1C_1D_1 are A_1(-2, 8), B_1(-2, 4), C_1(-8, 4), D_1(-8, 8). c) To find the image A_2B_2C_2D_2 of A_1B_1C_1D_1 under a reflection in the line y=1, we use the transformation rule (x, y) (x, 2k - y), where k=1. So the rule is (x, y) (x, 2(1) - y) = (x, 2 - y). Step 1: Apply the rule to point A_1(-2, 8). A_2 = (-2, 2 - 8) = (-2, -6) Step 2: Apply the rule to point B_1(-2, 4). B_2 = (-2, 2 - 4) = (-2, -2) Step 3: Apply the rule to point C_1(-8, 4). C_2 = (-8, 2 - 4) = (-8, -2) Step 4: Apply the rule to point D_1(-8, 8). D_2 = (-8, 2 - 8) = (-8, -6) The vertices of A_2B_2C_2D_2 are A_2(-2, -6), B_2(-2, -2), C_2(-8, -2), D_2(-8, -6). d) To find the image A_3B_3C_3D_3 of A_2B_2C_2D_2 under a reflection in the x-axis, we use the transformation rule (x, y) (x, -y). Step 1: Apply the rule to point A_2(-2, -6). A_3 = (-2, -(-6)) = (-2, 6) Step 2: Apply the rule to point B_2(-2, -2). B_3 = (-2, -(-2)) = (-2, 2) Step 3: Apply the rule to point C_2(-8, -2). C_3 = (-8, -(-2)) = (-8, 2) Step 4: Apply the rule to point D_2(-8, -6). D_3 = (-8, -(-6)) = (-8, 6) The vertices of A_3B_3C_3D_3 are A_3(-2, 6), B_3(-2, 2), C_3(-8, 2), D_3(-8, 6). That's 2 down. 3 left today — send the next one.