Question

The coordinates of an ordered pair have opposite signs. In which quadrant is the ordered pair lie? Explain.

Answer 1

If the coordinates of an ordered pair have opposite signs, it means that one coordinate is positive and the other is negative.

For example, the ordered pair (-3, 5) has opposite signs because -3 is negative and 5 is positive.

Since the signs of the coordinates are opposite, the ordered pair must lie in either the second or fourth quadrant of the cartesian plane. This is because the second and fourth quadrants are the only quadrants where x and y have opposite signs.

In the second quadrant, x is negative and y is positive. In the fourth quadrant, x is positive and y is negative.

So, to determine in which quadrant the ordered pair lies, we would need to know which coordinate is positive and which is negative. If the x-coordinate is negative and the y-coordinate is positive, the ordered pair lies in quadrant II. If the x-coordinate is positive and the y-coordinate is negative, the ordered pair lies in quadrant IV.