Q1. What are the axes called in the rectangular coordinate system, and how are points plotted?

Background

Topic: Rectangular (Cartesian) Coordinate System

This question is about understanding the basic structure of the coordinate plane, including the names of the axes and how to plot points using ordered pairs.

Key Terms and Formulas

• x-axis: The horizontal axis on the coordinate plane.

• y-axis: The vertical axis on the coordinate plane.

• Origin: The point where the x-axis and y-axis intersect, denoted as (0, 0).

• Ordered Pair: A pair of numbers (x, y) that represent a point's location on the plane.

Step-by-Step Guidance

1. Identify the two perpendicular lines that form the coordinate plane: the horizontal line is the x-axis, and the vertical line is the y-axis.

2. Understand that the intersection of these axes is called the origin, with coordinates (0, 0).

3. To plot a point, use an ordered pair (x, y): move x units left or right from the origin along the x-axis, then move y units up or down along the y-axis.

4. Remember that positive x-values are to the right of the origin, and negative x-values are to the left. Positive y-values are above the origin, and negative y-values are below.

Try solving on your own before revealing the answer!

Q2. Plot the points A(4, 3), B(–3, 2), C(–2, –3), D(5, –4), E(0, 0), F(0, –3) on the coordinate plane and identify the quadrant of each point.

Background

Topic: Plotting Points and Identifying Quadrants

This question tests your ability to plot points on the Cartesian plane and determine which quadrant each point is located in.

Key Terms and Formulas

• Quadrants: The coordinate plane is divided into four regions called quadrants:

  • Quadrant I: x > 0, y > 0

  • Quadrant II: x < 0, y > 0

  • Quadrant III: x < 0, y < 0

  • Quadrant IV: x > 0, y < 0

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

Step-by-Step Guidance

1. For each point, start at the origin (0, 0).

2. Move right for positive x or left for negative x, then move up for positive y or down for negative y.

3. Plot each point on the graph accordingly.

4. Determine the quadrant by checking the signs of x and y for each point.

Try solving on your own before revealing the answer!

Q3. Plot the points W(1, –2), X(5, 2), Y(–3, –4), Z(–4, 3) on the coordinate plane.

Background

Topic: Plotting Points

This question is about accurately plotting points with both positive and negative coordinates on the Cartesian plane.

Key Terms and Formulas

• Ordered Pair (x, y): Indicates the position of a point on the plane.

Step-by-Step Guidance

1. For each point, start at the origin (0, 0).

2. Move horizontally to the x-value, then vertically to the y-value.

3. Mark the location of each point on the graph.

Try solving on your own before revealing the answer!