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The Rectangles on the coordinate plane exercise appears under the 6th grade (U.S.) Math Mission and 8th grade (U.S.) Math Mission. This exercise analyzes information about rectangles using their coordinates in the Cartesian coordinate plane.

Types of Problems

There are two types of problems in this exercise:

  1. Find the coordinates of the missing point: The point is not really missing, it's coordinates are. A rectangle is drawn and the coordinates of three of the vertices are given. The student is asked to find the coordinates of the fourth corner.
    Rotcp1

    Find the coordinates of the missing point

  2. Use the coordinates to answer a question: This problem has no grid drawn, but does provide the coordinates of the four corners of a rectangle. The student is then asked to answer a question about the rectangle.
    Rotcp2

    Use the coordinates to answer a question

Strategies

Ability to visualize the coordinate plane or fast graphing skills can assist with doing this exercise well.

  1. All the rectangles have sides that are parallel to the axes. Therefore each x-coordinate and each y-coordinate will occur twice. This can allow the problem to be performed by analyzing which coordinates are not recorded twice.
  2. Research indicates that the problem Use the coordinates to answer a question are always about the length of a side. This could easily be expanded into questions such as area or perimeter in the future, so be wary.

Real-life Applications

  1. Architects use lots of geometry when building bridges, roofs on houses, and other structures.
  2. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.

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