4-6-year-old children were given problems in which they had to decide which 1 of an array of points was in line with 2 coordinate markers. The simplest problems had 4 points to choose between and markers perpendicular to the horizontal and vertical axes. Children of all ages were able to extrapolate lines from both coordinates to solve these problems. The older children were also given more complex problems. In some of these, 1 marker was at 45 degrees to an axis, the other perpendicular: in others the array was increased to 16 points and presented sometimes in a regular, sometimes in an irregular pattern. There were developmental improvements in performance, and the complex problems were more difficult than the simpler ones. However, 5- and 6-year-olds did extremely well even on the complex problems. The results establish that young children's grasp of Euclidean spatial relationships is more adequate than has often been suggested.