Comprehensive College Algebra Study Guide: Properties, Operations, Functions, and Graphs

Q45. In which quadrant or on which axis is each point located?

Background

Topic: Coordinate Plane & Quadrants

This question tests your understanding of the coordinate plane, including how to identify the location of points based on their coordinates.

Key Terms:

• Quadrant: The coordinate plane is divided into four quadrants by the x- and y-axes.

• Axis: The x-axis (horizontal) and y-axis (vertical) are the reference lines.

• Origin: The point (0,0) where the axes intersect.

Step-by-Step Guidance

1. Recall the quadrant layout: Quadrant I (x > 0, y > 0), Quadrant II (x < 0, y > 0), Quadrant III (x < 0, y < 0), Quadrant IV (x > 0, y < 0).

2. For each point, examine the signs of the x and y coordinates to determine its location.

3. If either coordinate is zero, the point lies on an axis (x = 0 is y-axis, y = 0 is x-axis).

4. Apply this reasoning to each point: (−3, −2), (−7, 5), (6, 7), (2.4, −3.1), (0, 8).

5. Write the quadrant or axis for each point, but stop before stating the final locations.

Try solving on your own before revealing the answer!

Final Answer:

• a. (−3, −2): Quadrant III

• b. (−7, 5): Quadrant II

• c. (6, 7): Quadrant I

• d. (2.4, −3.1): Quadrant IV

• e. (0, 8): y-axis

Each point's location is determined by the signs of its coordinates. If x and y are both positive, it's Quadrant I; if x is negative and y is positive, it's Quadrant II; if both are negative, it's Quadrant III; if x is positive and y is negative, it's Quadrant IV. If either coordinate is zero, the point lies on an axis.