Chapter 3, Problem 1RE

To determine

To find:

The set of all point which is lie in the $\left(x,y\right)$ in a coordinate plane such that $y/x<0$

Answer to Problem 1RE

The point $\left(x,y\right)$ in a coordinate plane such that $y/x<0$ Belong to the second or fourth quadrants

Explanation of Solution

Given:

The point $\left(x,y\right)$ in a coordinate plane such that $y/x<0$

Concept used:

An ordered pair $\left(x,y\right)$ of real numbers to each point in a plane

A rectangular or Cartesian coordinate system in a plane by mean of two perpendicular coordinates lines called coordinate axis

Calculation:

A real number (coordinate) to each point on a line

An ordered pair $\left(x,y\right)$ of real numbers to each point in a plane

A rectangular or Cartesian coordinate system in a plane by mean of two perpendicular coordinates lines called coordinate axis that intersect at the origin O

The plane is then a coordinate plane, or an $xy$ plane such that $y/x<0$

The coordinate axes divide the plane in to four parts called first, second, third, fourth quadrants

Points on the axes do not belong to any quadrant

So,

The point $\left(x,y\right)$ in a coordinate plane such that $y/x<0$ Belong to the second or fourth quadrants