Copyright © by Holt, Rinehart and Winston
Acc. Geom/Algebra II Name__________________________
Introduction to Coordinate Proof Period________Date______________
A coordinate proof is a proof that uses coordinate geometry and algebra.
In a coordinate proof, the first step is to position a figure in a plane. There
are several ways you can do this to make your proof easier.
Position each figure in the coordinate plane and give the coordinates of each vertex.
[pic] [pic]
1. a square with side lengths of 6 units 2.) a right triangle with leg lengths of 3 units
and 4 units
[pic] [pic]
3.) a triangle with a base of 8 units and 4.) a rectangle with a length of 6 units and
a height of 2 units a width of 3 units
You can prove that a statement about a figure is true without knowing the side lengths.
To do this, assign variables as the coordinates of the vertices.
[pic]
Position each figure in the coordinate plane and give the coordinates of each vertex.
[pic] [pic]
5.) a right triangle with leg lengths s and t 6.) a square with side lengths k
[pic] [pic]
7.) a rectangle with leg lengths ( and w 8.) a triangle with base b and height h
9.) Describe how you could use the formulas for midpoint and slope to prove the following.
Given: (HJK, R is the midpoint of [pic] S is the midpoint of [pic]
Prove: [pic]
_________________________________________________________________________________________
_________________________________________________________________________________________
Introduction to Coordinate Proof
ANSWERS
1.)
One possible answer on graph above.
2.)
One possible answer on graph above.
3.)
One possible answer on graph above.
4.)
One possible answer on graph above.
5.)
One possible answer on graph above.
6.)
One possible answer on graph above.
7.)
One possible answer on graph above.
8.)
One possible answer on graph above.
9.) Possible answer: Use the midpoint formula to find the coordinates of the midpoints R and S. Then use the coordinates and the formula for slope to find the slopes of [pic] and [pic].
-----------------------
|Positioning a Figure in the Coordinate Plane |
|Keep the figure in |Center the figure |
|Quadrant I by using |at the origin. |
|the origin as a vertex. | |
|Center a side of the |Use one or both axes |
|figure at the origin. |as sides of the figure. |
Continued on the back
a right triangle with leg lengths c and d
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