Problem 37 - Algebra 1: Concepts and Skills

Question

The point \((-9,-8)\) is in which quadrant? (A) Quadrant I (B) Quadrant II (C) Quadrant III (D) Quadrant IV

Step-by-Step Solution

Answer

The point \((-9,-8)\) is in Quadrant III (C).

Step 1: Analyze coordinates

The point \( (-9, -8) \) has both \( x < 0 \) and \( y < 0 \).

Step 2: Identify quadrant

When both coordinates are negative, the point is in Quadrant III. Answer: (C).

Key Concepts

Understanding Quadrants in the Coordinate Plane

When dealing with a coordinate plane, it's essential to understand how it is divided. The coordinate plane is split into four quadrants by the x-axis and y-axis. They meet at the origin, which is the point (0,0). Each quadrant is like a section of a city map, helping you locate positions precisely.

• Quadrant I: The top-right section where both x and y coordinates are positive, like (3,4).
• Quadrant II: The top-left section where x is negative, but y is positive, like (-3,4).
• Quadrant III: The bottom-left section where both x and y coordinates are negative, just like our example (-9,-8).
• Quadrant IV: The bottom-right section where x is positive and y is negative, such as (3,-4).

Knowing which quadrant a point is in can help in tasks like graphing, solving equations, or even programming.
It becomes handy to quickly visualize where a point sits on the plane.

The Role of Negative Coordinates

Negative coordinates indicate a specific direction on the coordinate plane.

• The x-coordinate tells us how far left or right the point is from the origin.
• The y-coordinate shows us how far up or down the point lies.

With negative coordinates, we move in the direction opposite to the positive axes.
For instance, an x-coordinate of -9 tells us that the point is 9 units to the left of the y-axis. Similarly, a y-coordinate of -8 means the point is 8 units below the x-axis.
In combination, these negative values place the point into Quadrant III, showcasing their importance in determining the point's exact location.

Graphing Points on the Coordinate Plane

Graphing points accurately on the coordinate plane involves both an understanding of coordinates and spatial awareness. Start by finding the spot where the x-coordinate aligns first.

• Move left or right based on the x-coordinate value. Negative means move left.
• Then move up or down from there, following the y-coordinate. For negative, go down.
• Plot the point at the intersection of these movements.

For the point (-9,-8), you'd start at the origin, go 9 steps left, and then 8 steps down.
Mark this location clearly. Visualization here helps in organizing data, understanding geometric concepts, or even in creating graphs for reports.
With practice, this process becomes second nature, allowing you to quickly sketch points and figures on the plane.