Answer:
a) [tex](a,b)[/tex]
Given that [tex]a> 0[/tex] and [tex]b > 0[/tex], the point is located between the +x and +y semiaxes.
b) [tex](-a, b)[/tex]
Given that [tex]-a < 0[/tex] and [tex]b> 0[/tex], the point is located between the -x and +y semiaxes.
c) [tex](a, -b)[/tex]
Given that [tex]a > 0[/tex] and [tex]-b< 0[/tex], the point is located between the +x and -y semiaxes.
d) [tex](-a, -b)[/tex]
Given that [tex]-a < 0[/tex] and [tex]-b < 0[/tex], the point is located between the -x and -y semiaxes.
Step-by-step explanation:
All points are represented in rectangular form, that is, numbers of the form [tex](x, y)[/tex] and in which the following conditions are known:
1) If [tex]x < 0[/tex], then the point is located in the -x semiaxis, otherwise it is located in the +x semiaxis.
2) If [tex]y < 0[/tex], then the point is located in the -y semiaxis, otherwise it is located in the +y semiaxis.
Then, we proceed to analyze each case below:
a) [tex](a,b)[/tex]
Given that [tex]a> 0[/tex] and [tex]b > 0[/tex], the point is located between the +x and +y semiaxes.
b) [tex](-a, b)[/tex]
Given that [tex]-a < 0[/tex] and [tex]b> 0[/tex], the point is located between the -x and +y semiaxes.
c) [tex](a, -b)[/tex]
Given that [tex]a > 0[/tex] and [tex]-b< 0[/tex], the point is located between the +x and -y semiaxes.
d) [tex](-a, -b)[/tex]
Given that [tex]-a < 0[/tex] and [tex]-b < 0[/tex], the point is located between the -x and -y semiaxes.
