Math Problem Statement

What are the coordinates of points C, D, E, and F on the rectangular shape shown in the Cartesian plane, and how can we calculate its perimeter and area?

Solution

The image shows a rectangular shape plotted on a Cartesian coordinate plane. The vertices of the rectangle are labeled as CC, DD, EE, and FF. Based on the grid lines and the visible points, the coordinates of each vertex appear to be approximately as follows:

  • C(6,8)C (-6, -8)
  • D(2,8)D (-2, -8)
  • E(2,2)E (-2, -2)
  • F(6,2)F (-6, -2)

Would you like to confirm the exact coordinates of each point or need help with a specific mathematical task related to this shape (e.g., finding area, perimeter, transformations, etc.)?

Here are some questions to explore based on the figure:

  1. What is the perimeter of the rectangle?
  2. How do we calculate the area of this rectangle?
  3. What are the midpoints of each side of the rectangle?
  4. If this rectangle is reflected across the y-axis, what are the new coordinates of its vertices?
  5. What would be the effect of translating the rectangle 3 units to the right and 2 units up?

Tip: Remember, the formula for finding the area of a rectangle is Area=length×width\text{Area} = \text{length} \times \text{width}.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Perimeter
Area
Transformations

Formulas

Perimeter of a rectangle: P = 2(l + w)
Area of a rectangle: A = l * w
Midpoint of a line segment: M = ((x1 + x2) / 2, (y1 + y2) / 2)
Reflection across the y-axis: (x, y) -> (-x, y)
Translation: (x, y) -> (x + a, y + b)

Theorems

Reflection theorem
Midpoint theorem

Suitable Grade Level

Grades 6-8