In the Euclidean plane, the points which have rational x and y coordinates are rational. For example P(0,1) or P(-4,1/3) are rational points, by definition. P(sqrt(2),5) isn’t, since the x coordinate is an irrational number.
You probably know, that every circle on this plane covers an infinite number of rational points.
What you probably don’t know, is that most lines in this plane, don’t intersect with a single rational point. Most lines on the plane go exclusively through irrational points!