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									                    Ohio Graduation Test for Mathematics – March 2005
                                   Annotated Item 41

Standard and Benchmark Assessed:

Standard: Geometry and Spatial Sense
Benchmark: D. Use coordinate geometry to represent and examine the properties of geometric

Multiple Choice Question:

41. An electronics engineer is programming the compute r that controls the
    circuit boar d cutting tools. He enters the coordinates of the vertices of a
    rectangular circuit board. The f irst three coordinates are (2, 0), (2, 6) and
    (6, 6).

     W hat are the coordinates of the f ourth vertex?

     A.    (0, 2)
     B.    (0, 6)
     C.    (6, 0)
     D.    (6, 2)

This multiple-choice question asks students to determine the fourth coordinate pair of a
rectangle when given the first three coordinate pairs for the rectangle. The student can solve
this question graphically or by mathematical reasoning. The points (2,0) and (2,6) align
vertically, the points (2,6) and (6,6) align horizontally so the missing coordinate must align
horizontally with point (2,0) and vertically with the point (6,6) making the coordinates of the
fourth vertex (6,0). Graphically the student can plot the three given points and try each of the
points given in choices A, B, C and D. Choice C, (6,0), will be the fourth vertex of the rectangle.

Source: Ohio Department of Education                                                        July 05
                  Ohio Graduation Test for Mathematics – March 2005
                                 Annotated Item 41

The level of complexity for this question is Low Complexity, as students are required to recall
the properties of a rectangle and determine the fourth vertex and its coordinates

Performance Data:
The percent of public school students selecting answer choice C for question 41 on the March
2005 Ohio Graduation Test was 71%.

Key Words: coordinates, vertex, rectangle

Source: Ohio Department of Education                                                       July 05

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