IM Geo.6.14 Lesson: Coordinate Proof
Which one doesn’t belong?
A B 
C D 
A quadrilateral has vertices , , , and . What type of quadrilateral is it? Explain or show your reasoning.
Find the perimeter of this quadrilateral.
Find the area of this quadrilateral.
A parallelogram has vertices , , , and . Find the area of this parallelogram.
Consider a general parallelogram with vertices , , , and , where , , , and are positive. Write an expression for its area in terms of , , , and .
Use the applet to answer the questions.
First, observe and describe the image: What kind of line is in reference to the circle?
What does the measurement of angle appear to be?
Move point around. How does the measurement of angle appear to change? Use a corner of the index card to compare the size of the angle as it moves.
Move point to a location with integer coordinates. Each student in the group should choose a different spot for . Calculate the slopes of segments and . What do your results tell you?
Now select the button labeled “slopes.” This will show the slopes of and and their product. Move point around. What do you notice about the product of the slopes?
Based on the results, write a conjecture that captures what you are seeing.