Final Answer:
(i) The coordinates (-7, 102) are located in the second quadrant.
(ii) The coordinates (99, 999) are located in the first quadrant.
(iii) The coordinates (9, -63) are located in the fourth quadrant.
(iv) The coordinates (-23, -21) are located in the third quadrant.
Step-by-step explanation:
In the Cartesian coordinate system, the signs of the coordinates determine the quadrant in which a point lies. The first coordinate (x) represents the horizontal position, and the second coordinate (y) represents the vertical position.
(i) For (-7, 102), the x-coordinate is negative, and the y-coordinate is positive. This places the point in the second quadrant.
(ii) In the case of (99, 999), both x and y coordinates are positive, indicating the first quadrant.
(iii) With coordinates (9, -63), the x-coordinate is positive, and the y-coordinate is negative, placing the point in the fourth quadrant.
(iv) Finally, for the coordinates (-23, -21), both x and y coordinates are negative, assigning the point to the third quadrant.
Understanding the signs of coordinates and their relation to quadrants is crucial in determining the position of points on the coordinate plane. The quadrants are numbered in a counterclockwise order, starting from the positive x-axis. Each quadrant has specific characteristics based on the signs of the coordinates, aiding in graphical representation and analysis of mathematical relationships.