Concept Check Graph the points on a coordinate system and identify the quadrant or axis for each point. (-7, -4)

Verified step by step guidance

1. Step 1: Understand the coordinate system, which consists of four quadrants divided by the x-axis (horizontal) and y-axis (vertical).
2. Step 2: Identify the signs of the coordinates. The point (-7, -4) has a negative x-coordinate and a negative y-coordinate.
3. Step 3: Recall the quadrant rules: Quadrant I has positive x and y, Quadrant II has negative x and positive y, Quadrant III has negative x and y, and Quadrant IV has positive x and negative y.
4. Step 4: Determine the quadrant for the point (-7, -4). Since both coordinates are negative, the point is located in Quadrant III.
5. Step 5: Plot the point (-7, -4) on the coordinate system by moving 7 units left along the x-axis and 4 units down along the y-axis.

Key Concepts

Coordinate System

A coordinate system is a two-dimensional plane defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding this system is crucial for locating points accurately.

Quadrants

The coordinate plane is divided into four quadrants based on the signs of the x and y coordinates. Quadrant I contains points where both coordinates are positive, Quadrant II has a negative x and positive y, Quadrant III has both negative coordinates, and Quadrant IV has a positive x and negative y. Identifying the correct quadrant helps in understanding the location of points.

Axes

The axes in a coordinate system are the two perpendicular lines that define the plane. The x-axis runs horizontally, while the y-axis runs vertically. Points that lie directly on an axis have one coordinate equal to zero, which is essential for determining whether a point is on the x-axis, y-axis, or in one of the quadrants.