Section 6.8- Applying Coordinate Geometry
Essential Question: How can we use variables to complete coordinate geometry proofs
for general cases?
Do Now:
Coordinates for D:
Hint: Think about the properties of parallelograms to find the coordinates! There are 3
possible coordinates!
Helpful Hints for Placing a Figure in the Coordinate Plane

Place at least one side on an _________________ or at the _______________

Think about what you have to do next

Remember the properties of quadrilaterals (see attached checklist)
Example 1: Naming Coordinates
What are the coordinates of the vertices of each figure?
a.
b.
S= __________
Q= _________
R= __________
E= _________
c.
T=
________
R= _______
I= _______
d.
R= __________
E= _________
K= __________
I= _________
C= __________
T= _________
T= __________
E= _________
e. Why do some sets of coordinates have more variables than others?
Example 2- Using Variable Coordinates
The diagram shows a general
parallelogram with a vertex at the origin
and one side along the x-axis.
a. What are the coordinates of D, the point of intersection of the diagonals of
ABCD?
HINT: Think about the properties of diagonals in a parallelogram.
b. Explain why the x-coordinate of B is the sum of 2a and 2b.
c. The diagram shows a trapezoid with the base centered at the origin. Is the
trapezoid isosceles? Explain.
Example 3: Planning a Coordinate Proof
Plan a coordinate proof of the Triangle Midsegment Theorem.
Recall: A midsegment connects __________________________. The triangle misegment
theorem states that if a segment joins the ___________ of two sides of a triangle, then
the segment is ______________ to the third side and it is
_____________________________.
Given:
E is the _______________________________;
F is the ___________________________
Prove: ______________________ and __________________________
Create a plan on how to prove the triangle midsegment theorem. Specify which
formulas you need to use and why.
Group Work:
1. What are the coordinates of the vertices of each figure?
a.
3.
HW: p. 410-411 #7-9, 13, 17-19, 22
b.