Question

A point has one positive coordinate and one negative coordinate. Can you determine in which quadrant the point lies? Explain.

Short answer

The point will lie either in Quadrant II or in Quadrant IV.

Step-by-step solution

What is a coordinate system? 

A Rectangular or Cartesian coordinate system in two dimensions (x and y) is defined by an ordered pair of perpendicular lines or axes.

Points are placed by their distance along a horizontal (x) and vertical (y) axis from the origin, defined as (0, 0).

Coordinate of the Origin

It has zero distance from both the axes. Hence the coordinates of the origin are (0, 0).

Sign convention of all quadrants:

1^st quadrant: x – positive and y – positive

2^nd quadrant: x – negative and y – positive

3^rd quadrant: x – negative and y – negative

4^th quadrant: x – positive and y – negative

Coordinate Geometry in Two Dimensional Plane

Incoordinate geometry, first, we learn about locating the points in a X – Y coordinate plane.

For example, the point (2, 3) is 3 units away from the X−axis measured along the positive X−axis and 2 units away from Y−axis measured along the positive Y−axis.

The points having x-coordinate as ‘0′ lies on the Y−axis and the points having Y-coordinate as ‘0’ lies on the X−axis

For example, the points (2, 0), (5, 0) lies on X−axis and the points (0, −3), (0, 7) lies on Y−axis

Step 3: A point has one positive coordinate and one negative coordinate. Can you determine in which quadrant the point lies? Explain.

Sign convention of all quadrants:

1^st quadrant: x – positive and y – positive

2^nd quadrant: x – negative and y – positive

3^rd quadrant: x – negative and y – negative

4^th quadrant: x – positive and y – negative

The statement provided by the question,

A point has a positive coordinate and a negative coordinate.

The point lies either in Quadrant II or in Quadrant IV. Because Quadrant I have both x and y coordinates as positive and Quadrant III has both x and y coordinates as negative.

The point will lie either in Quadrant II or in Quadrant IV.