Math Problem Statement

Three points are marked on the coordinate grid. Find the coordinates of a fourth point so that the four points form the vertices of a rectangle.

Solution

To solve this problem, we need to identify the coordinates of a fourth point that will form a rectangle with the three marked points.

Step-by-step solution:

The three points marked on the grid are approximately:

  • Point A: (-4, 5)
  • Point B: (2, 5)
  • Point C: (-4, -5)

These three points can be seen as the three vertices of a rectangle. Now, let's find the fourth point, Point D.

  1. Observing the vertical and horizontal alignment:

    • Points A and B are horizontally aligned (same y-coordinate: 5).
    • Points A and C are vertically aligned (same x-coordinate: -4).
  2. Using symmetry to find Point D:

    • Since Points A and C are vertically aligned, the fourth point (Point D) must be horizontally aligned with Point C, meaning Point D should have the same y-coordinate as Point C, which is -5.
    • Since Points B and A are horizontally aligned, Point D must have the same x-coordinate as Point B, which is 2.

Thus, the coordinates of the fourth point are: D(2,5)D(2, -5)

This point completes the rectangle.

Final Answer:

The coordinates of the fourth point are (2,5)(2, -5).

Would you like a detailed breakdown of how rectangles are formed on a coordinate plane, or do you have further questions? Here are some related questions to consider:

  1. How can we use the midpoint to verify a rectangle on a coordinate plane?
  2. How do we calculate the area of a rectangle using coordinates?
  3. What is the difference between a square and a rectangle in terms of coordinate geometry?
  4. How can we find the perimeter of the rectangle formed by these four points?
  5. What would change if the figure were a parallelogram instead of a rectangle?

Tip: When solving geometric problems on a coordinate grid, always check for patterns in the alignment of points (e.g., identical x- or y-coordinates) to find missing vertices.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Rectangles
Symmetry

Formulas

Coordinate symmetry for rectangles

Theorems

Rectangle properties on a coordinate plane

Suitable Grade Level

Grades 6-8