Question

a coordinate plane is formed by the intersection of two number lines called the x - axis and y - axis. the coordinate plane is divided into four quadrants.
an ordered pair is a pair of numbers used to locate a point on a coordinate plane. the first number of the pair is the x - coordinate, and the second number is the y - coordinate.
the ordered pair for the point on the coordinate plane on the right is (2, - 1).
the intersection of the axes is at 0 on both number lines and is called the origin.
the origin is located at the ordered pair (0, 0).

Explanation:

Step1: Analyze the problem context

The problem is about the coordinate plane, which involves concepts like ordered pairs, axes, origin, and quadrants. This falls under the subfield of Geometry in Mathematics as it deals with the study of points, lines, and planes in a coordinate system.

Step2: Identify the key concepts

• A coordinate plane is formed by the intersection of the x - axis and y - axis.
• An ordered pair \((x,y)\) is used to locate a point, where \(x\) is the x - coordinate and \(y\) is the y - coordinate.
• The origin is at \((0,0)\), the intersection of the x - axis and y - axis.
• The point \((2,- 1)\) is in Quadrant IV (since \(x = 2>0\) and \(y=-1 < 0\)).

Answer:

The subfield is Geometry (under Mathematics) as the problem deals with the coordinate plane, points, axes, and their properties which are core concepts of Geometry.