if the point (a b) is in the fourth quadrant in what quadrant is (-a,-b)

"if the point (a, b) is in the fourth quadrant" then the point could be something like (6, -5) which is one of infinitely many examples. So we see that a = 6 and b = -5. Any point in quadrant 4 has a positive x coordinate and negative y coordinate.

Since (a,b) = (6,-5), this means (-a, -b) = (-6, -(-5)) = (-6, 5) which is in quadrant 2. Any point in quadrant 2 has a negative x coordinate and positive y coordinate.

The quadrant diagram is shown below, as well as the points mentioned.

Side note: The rule [tex](x,y) \to (-x,-y)[/tex] represents a rotation of 180 degrees around the origin.

MrRoyal MrRoyal · Answer 2 · 2021-10-19T14:11:53+02:00

There are four quadrants in a coordinate plane

Point (-a,-b) is in the second quadrant

The given parameter is:

[tex]\mathbf{(x,y) = (a,b)}[/tex]

When a point is rotated by 180 degrees, the coordinates of the point get negated.

i.e. the rule of 180 degrees rotation is:

[tex]\mathbf{(x,y) \to (-x,-y)}[/tex]

Substitute a and b for x and y

[tex]\mathbf{(a,b) \to (-a,-b)}[/tex]

This means that: (-a,-b) is (a,b) rotated by 180 degrees

The second quadrant is 180 degrees from the fourth quadrant.

Hence, point (-a,-b) is in the second quadrant