Math Problem Statement

Graph these points in the coordinate plane: (-2, 3), (2, 3), (-2, -3), (2, -3). Connect all of the points. Describe the figure.

Solution

The problem asks you to graph four points on the coordinate plane:

  • (-2, 3)
  • (2, 3)
  • (-2, -3)
  • (2, -3)

Step-by-Step Instructions:

  1. Plot the Points:

    • Point (-2, 3): Start at the origin (0,0), move 2 units to the left (because of the -2), and 3 units up.
    • Point (2, 3): Start at the origin, move 2 units to the right, and 3 units up.
    • Point (-2, -3): Start at the origin, move 2 units to the left, and 3 units down.
    • Point (2, -3): Start at the origin, move 2 units to the right, and 3 units down.
  2. Connect the Points:

    • Connect these four points in sequence: (-2, 3), (2, 3), (2, -3), and (-2, -3).

    This should form a rectangle. The rectangle's sides are parallel to the x-axis and y-axis, with a width of 4 units (from x = -2 to x = 2) and a height of 6 units (from y = 3 to y = -3).

Would you like more details on graphing, or have any other questions?

Here are five related questions to expand on this concept:

  1. What are the coordinates of the midpoints of each side of the rectangle?
  2. How can you find the area of this rectangle using the points?
  3. How do you find the distance between two points, such as (-2, 3) and (2, 3)?
  4. If the rectangle were rotated by 45 degrees, what would the new coordinates of the points be?
  5. How would the coordinates change if the rectangle was translated 3 units to the right?

Tip: When plotting points, always start at the origin and carefully move according to the signs of the coordinates.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Graphing Points
Shapes on the Coordinate Plane

Formulas

Distance between two points
Area of a rectangle

Theorems

Coordinate geometry rules for rectangles

Suitable Grade Level

Grade 6