1. **Problem Statement:** Find the coordinates of point U given points Z(-4,0), G(-4,-6), and C on segment ZG such that C divides ZG in a certain ratio, and U lies on a line from C with given segment lengths. 2. **Given:** - Z = (-4,0) - G = (-4,-6) - C lies between Z and G, with CG = 2.4 (distance from C to G) - CU = 9 (distance from C to U) 3. **Step 1: Find coordinates of C.** Since Z and G have the same x-coordinate (-4), segment ZG is vertical. Length ZG = $|0 - (-6)| = 6$ C divides ZG such that CG = 2.4, so CZ = $6 - 2.4 = 3.6$ Using section formula for vertical segment: $$y_C = y_Z - CZ = 0 - 3.6 = -3.6$$ Coordinates of C: $(-4, -3.6)$ 4. **Step 2: Find coordinates of U.** U lies on a line from C horizontally to the right (positive x direction), so $y_U = y_C = -3.6$ Distance CU = 9, so $$x_U = x_C + 9 = -4 + 9 = 5$$ 5. **Final answer:** $$U = (5, -3.6)$$ This means point U is at coordinates (5, -3.6).