Problem 2 Using Variable Coordinates
The diagram shows a general parallelogram with a vertex at the origin and one side along the x-axis. What are the coordinates of D, the point of intersection of the diagonals of
| Know | Need | Plan |
|---|---|---|
|
The coordinates of D | Since the diagonals of a parallelogram bisect each other, the midpoint of each segment is their point of intersection. Use the Midpoint Formula to find the midpoint of one diagonal. |
Use the Midpoint Formula to find the midpoint of
The coordinates of the point of intersection of the diagonals of
✓ Got It?
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- Reasoning In Problem 2, explain why the x-coordinate of B is the sum of 2a and 2b.
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The diagram below shows a trapezoid with the base centered at the origin. Is the trapezoid isosceles? Explain.
You can use coordinate geometry and algebra to prove theorems in geometry. This kind of proof is called a coordinate proof. Sometimes it is easier to show that a theorem is true by using a coordinate proof rather than a standard deductive proof. It is useful to write a plan for a coordinate proof. Problem 3 shows you how.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs