In which quadrants could a point be located if its coordinates are reciprocals to each other
To determine the possible quadrants in which a point could be located if its coordinates are reciprocals to each other, we need to consider the signs of the coordinates.
Reciprocal of a number is obtained by dividing 1 by the number. Let's assume the coordinates of the point are (x, y), where x and y are reciprocals of each other.
If the x-coordinate is positive, then the reciprocal of x will also be positive. In this case, the y-coordinate must be negative since reciprocals have opposite signs. Therefore, the point could be located in either the third quadrant (where both x and y are negative) or the fourth quadrant (where x is positive and y is negative).
Similarly, if the x-coordinate is negative, then the reciprocal of x will be negative. In this scenario, the y-coordinate must be positive for the same reason. Consequently, the point could be located in either the first quadrant (where both x and y are positive) or the second quadrant (where x is negative and y is positive).
In summary, a point with reciprocals for coordinates could be located in any of the four quadrants (i.e., the first, second, third, or fourth quadrant), depending on the signs of its coordinates.
Think about it
if y = 1/x, then either they are both positive or both negative. That's 1st and 3rd quadrants.