1. **State the problem:** We have triangle ABC with points A(2,3), B(7,1), and C(1,1). It is enlarged about the origin with a scale factor of $-2$ to form triangle A'B'C'. We need to find the coordinates of A' and B'. 2. **Formula for enlargement about the origin:** If a point $P(x,y)$ is enlarged by a scale factor $k$ about the origin, the image point $P'(x',y')$ is given by: $$ x' = kx, \quad y' = ky $$ 3. **Apply the scale factor $k = -2$ to points A and B:** - For $A(2,3)$: $$ A' = (-2 \times 2, -2 \times 3) = (-4, -6) $$ - For $B(7,1)$: $$ B' = (-2 \times 7, -2 \times 1) = (-14, -2) $$ 4. **Interpretation:** The negative scale factor means the image is not only enlarged by a factor of 2 but also reflected through the origin, placing A' and B' in the opposite quadrant. **Final answer:** $$ A' = (-4, -6), \quad B' = (-14, -2) $$