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 are the solutions to problems 7 and 8. 7. Triangle ABC has vertices A(1,2), B(4,2), C(1,4). Draw the triangle and state the coordinates of the image A',B',C' generated under a rotation of 90^ about the origin (0,0). To rotate a point (x,y) by 90^ about the origin (0,0), the new coordinates are (-y,x). Step 1: Apply the rotation rule to each vertex. For A(1,2): A' = (-2, 1) For B(4,2): B' = (-2, 4) For C(1,4): C' = (-4, 1) Step 2: State the coordinates of the image. The coordinates of the image are A'(-2,1), B'(-2,4), and C'(-4,1). (Since I cannot draw on the provided grid, I am providing the coordinates of the image.) The final answer is A'(-2,1), B'(-2,4), C'(-4,1). 8. Given that a = 3 \\ -5 and b = 5 \\ -15 , find (1)/(4)(b + a). Step 1: Add the vectors b and a. b + a = 5 \\ -15 + 3 \\ -5 b + a = 5+3 \\ -15+(-5) b + a = 8 \\ -20 Step 2: Multiply the resulting vector by the scalar (1)/(4). (1)/(4)(b + a) = (1)/(4) 8 \\ -20 (1)/(4)(b + a) = (1)/(4) × 8 \\ (1)/(4) × (-20) (1)/(4)(b + a) = 2 \\ -5 The final answer is 2 \\ -5 . 3 done, 2 left today. You're making progress.