Remarks
Coordinate geometry is used while students prove quadrilaterals to be congruent, similar, or regular.
Coordinate geometry is used to prove properties of quadrilaterals.
Example: Given a quadrilateral with vertices (0, 0), (5/2, 5sqrt(3)/2), (5, 0), (7, 7sqrt(3)/3), prove that the diagonals of this quadrilateral are perpendicular.
Example: Is rectangle ABCD with vertices at A(0, 0), B(4, 0), C(4, 2), D(0, 2) congruent to rectangle PQRS with vertices at P(-2, -1), Q(2, -1), R(2, 1), S(-2, 1)? Justify your answer.
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Item Type(s):
This benchmark may be assessed using:
MC
item(s)
- Clarification :
Students will use coordinate geometry and geometric properties to justify measures and characteristics of congruent, regular, and similar quadrilaterals. - Content Limits :
Items may include statements and/or justifications to complete formal and informal proofs.
Items may include the use of coordinate planes.
- Stimulus Attributes :
Graphics should be used for most of these items, as appropriate.
Items may be set in either real-world or mathematical contexts.
- Test Item #: Sample Item 1
- Question:
On the coordinate grid below, quadrilateral ABCD has vertices with integer coordinates.
Quadrilateral QRST is similar to quadrilateral ABCD with point S located at (5, -1) and point T located at (-1, -1). Which of the following could be possible coordinates for point Q?
- Difficulty: N/A
- Type: MC: Multiple Choice