5.7: Proofs Using Coordinate Geometry

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5.7 Proofs Using Coordinate Geometry

• Expectations
• G1.1.5 Given a line segment in terms of its
  endpoints in the coordinate plane, determine its
  length and midpoint.
• G1.4.1 Solve multistep problems and construct
  proofs involving angle measure, side length,
  diagonal length, perimeter, and area of squares,
  rectangles, parallelograms, kites, and
  trapezoids.
• G1.4.2 Solve multistep problems and construct
  proofs involving quadrilaterals (e.g., prove that
  the diagonals of a rhombus are perpendicular)
  using Euclidean methods or coordinate geometry.

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• In the standard (x,y) coordinate plane, point X
  has coordinates (-4,0) and point Y has
  coordinates (0,-8). What are the coordinates of
  the midpoint of XY?
• (-6, -1)
• (-2, -4)
• (0, 2)
• (2, 4)
• (6, -1)

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Locating figures on the coordinate grid for
coordinate proofs

• - use the origin
• - use at least one axis for a side of the
  polygon.
• - if possible try to keep the figure in quadrant
  i unless it has reflection symmetry then use
  quadrants i and ii.

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• Locate a rectangle on the coordinate grid and
  label the coordinates of the vertices. The only
  numerical coordinate you may use is 0.

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• Locate a parallelogram on the coordinate grid and
  label the coordinates of its vertices. The only
  numerical coordinate you may use is 0.

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• Locate an isosceles triangle on the coordinate
  grid and label the coordinates of its vertices.
  The only numerical coordinate you may use is 0.

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• Given each set of vertices, determine whether
  parallelogram ABCD is a rhombus, a rectangle, or
  a square. List all that apply.
• A(1,5), B(6,5), C(6,10), D(1,10)

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Coordinate Proofs

• Prove a triangle midsegment is parallel to and
  one half the length of the third side of the
  triangle.
• Remember a midsegment is a segment whose
  endpoints are the midpoints of 2 sides of a
  triangle.

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Assignment

• pages 350-352,
• numbers 11-27, 32a