§43. The coordinates of a point in the plane

A Grade 9 topic in Geometry: “§43. The coordinates of a point in the plane” (pp. 168–170, I. B. Bekboev, A. A. Borubaev, A. A. Ayylchiev). In the plane we take two mutually perpendicular axes that meet at the point O. The horizontal axis is denoted x and called the x-axis (axis of abscissas), and the vertical one is denoted y and called the y-axis (axis of ordinates). The point O is called the origin. Two perpendicular axes with an origin and a unit of scale form the rectangular Cartesian coordinate system in the plane, written briefly as the xOy system. The coordinate axes divide the plane into four parts — quadrants. The number x is called the abscissa of the point M and y its ordinate; the point is written M(x, y). In quadrant I x>0, y>0; in II x<0, y>0; in III x<0, y<0; in IV x>0, y<0. The coordinates of O are O(0; 0). The coordinates of the midpoint N of the segment PQ are given by x=(x₁+x₂)/2, y=(y₁+y₂)/2.