Help! So confused! :(

Question

can someone walk me through this?

 

suppose the coordinate (a,b) is in q4. describe the location of the following points. (b,a), (2a,-2b), and (-b, -a). explain your reasoning.

Answer 1

In quadrant 4, you have (a, b)

 

where:

a is positive

b is negative

 

Lets assign numbers for a and b.  Then plug them in the following points.

 

a = 1

b = -1

 

(b, a) = (-1, 1)  ---> location is quadrant 2

 

(2a, -2b) = (2(1), -2(-1)) = (2, 2)  ----->  location is quadrant 1

 

(-b, -a) = (-(-1), -1) = (1, -1)  ------> location is quadrant 4

Answer 2

The quadrants are labeled in counter clockwise fashion as such

 

      II          |          I

     (-,+)      |       (+,+)

                  |

__________|___________

                  |

     III         |        IV

    (-,-)        |      (+,-)

                  |

 

Quadrant 1  all x and y values are both positive

Quadrant 2,  x values are negative, y values positive

Quadrant 3, all x and y values are negative

Quadrant 4, x values are positive, y values are negative

 

Since (a,b) is in quadrant 4 then a is positive, b is negative

or a>0, b<0

 

(b,a) = (-,+) so quadrant 2

 

(2a,-2b) = 

     2a = 2(pos #) is positive

     -2b = -2(neg #) is positive

(2a,-2b) = (+,+) = quadrant 1

 

(-b,-a) =

      -b = -(neg #) = +

      -a = -(pos #) = -

(-b,-a) = (+,-) = quadrant 4

Answer 3

Hi Lexi.

 

Q4 means the 4th quadrant, which in your X-Y plane means the lower right-hand corner.

 

II  | I

---+---

III | IV

 

In this quadrant X is positive and Y is negative. If (a,b) is in the 4th quadrant, that means that "a" has a (+) value and "b" has a (-) value. That will help us figure out our other points.

 

(b,a): Since we know b is negative and a is positive, we need to find out which quadrant is negative X and positive Y. This would be Quadrant II.

 

(2a, -2b): Again, a is positive and b is negative. Since we now have -2b, that means that the y-value will be a negative of a negative, which is positive. The "a" remains untouched in terms of sign, so it remains positive. So in this scenario, we have a positive X and a positive Y, which corresponds to Q1.

 

(-b, -a): If b is negative, a negative b gives a positive number, so we know our X-coordinate is positive. If a is positive, then we know that -a must be a negative number, which gives us a negative Y-coordinate. Positive X and negative Y occurs in the 4th Quadrant.

 

Hope this helps.