Question

13. ABSTRACT REASONING Let a and b be positive real numbers. Describe how to plot

(a, b), (-a, b),(a, -b), and (-a, -b).

Answer 1

a)
`(a,b)`

Given that
`a> 0` and
`b > 0`, the point is located between the +x and +y semiaxes.

b)
`(-a, b)`

Given that
`-a < 0` and
`b> 0`, the point is located between the -x and +y semiaxes.

c)
`(a, -b)`

Given that
`a > 0` and
`-b< 0`, the point is located between the +x and -y semiaxes.

d)
`(-a, -b)`

Given that
`-a < 0` and
`-b < 0`, the point is located between the -x and -y semiaxes.

Explanation:

All points are represented in rectangular form, that is, numbers of the form
`(x, y)` and in which the following conditions are known:

1) If
`x < 0`, then the point is located in the -x semiaxis, otherwise it is located in the +x semiaxis.

2) If
`y < 0`, 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)
`(a,b)`

Given that
`a> 0` and
`b > 0`, the point is located between the +x and +y semiaxes.

b)
`(-a, b)`

Given that
`-a < 0` and
`b> 0`, the point is located between the -x and +y semiaxes.

c)
`(a, -b)`

Given that
`a > 0` and
`-b< 0`, the point is located between the +x and -y semiaxes.

d)
`(-a, -b)`

Given that
`-a < 0` and
`-b < 0`, the point is located between the -x and -y semiaxes.