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: Identify the coordinates of the original triangle and the center of enlargement. The original triangle has vertices A(-1, -1), B(-1, -4), and C(-3, -2). The center of enlargement is O(2, 1). The scale factor is k=2. Step 2: Calculate the coordinates of the enlarged triangle using the formula for enlargement. For a point (x, y) enlarged from a center (x_c, y_c) with a scale factor k, the new point (x', y') is given by: x' = x_c + k(x - x_c) y' = y_c + k(y - y_c) For point A(-1, -1): x_A' = 2 + 2(-1 - 2) = 2 + 2(-3) = 2 - 6 = -4 y_A' = 1 + 2(-1 - 1) = 1 + 2(-2) = 1 - 4 = -3 So, A' = (-4, -3). For point B(-1, -4): x_B' = 2 + 2(-1 - 2) = 2 + 2(-3) = 2 - 6 = -4 y_B' = 1 + 2(-4 - 1) = 1 + 2(-5) = 1 - 10 = -9 So, B' = (-4, -9). For point C(-3, -2): x_C' = 2 + 2(-3 - 2) = 2 + 2(-5) = 2 - 10 = -8 y_C' = 1 + 2(-2 - 1) = 1 + 2(-3) = 1 - 6 = -5 So, C' = (-8, -5). The coordinates of the enlarged triangle are A'(-4, -3), B'(-4, -9), and C'(-8, -5). Step 3: Draw the triangles on the Cartesian plane. • Draw the x-axis and y-axis on the grid provided. • Plot the center of enlargement O(2, 1). • Plot the vertices of the original triangle: A(-1, -1), B(-1, -4), and C(-3, -2). Connect these points to form triangle ABC. • Plot the vertices of the enlarged triangle: A'(-4, -3), B'(-4, -9), and C'(-8, -5). Connect these points to form triangle A'B'C'. The coordinates of the original triangle are: A = (-1, -1) B = (-1, -4) C = (-3, -2) The coordinates of the enlarged triangle are: A' = (-4, -3) B' = (-4, -9) C' = (-8, -5) The center of enlargement is O = (2, 1).