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.

04/21/23 5.7: Coordinate Proofs

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?

A. (-6, -1)

B. (-2, -4)

C. (0, 2)

D. (2, 4)

E. (6, -1)

04/21/235.7: Coordinate Proofs

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.

04/21/235.7: Coordinate Proofs

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

04/21/235.7: Coordinate Proofs

04/21/235.7: Coordinate Proofs

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

04/21/235.7: Coordinate Proofs

04/21/235.7: Coordinate Proofs

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

04/21/235.7: Coordinate Proofs

04/21/235.7: Coordinate Proofs

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)

04/21/235.7: Coordinate Proofs

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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.

04/21/235.7: Coordinate Proofs

Assignment

pages 350-352,

numbers 11-27, 32a

04/21/235.7: Coordinate Proofs