Page 1 of 5. 1.1 RECTANGULAR COORDINATES. Objectives. Plot points in the Cartesian plane. Use the distance formula to fi
1.1 RECTANGULAR COORDINATES Objectives Plot points in the Cartesian plane. Use the distance formula to find the distance between two points. Use the midpoint formula to find the midpoint of a line segment. Use the Cartesian plane to model and solve real-life problems.
The Cartesian Plane * Draw the Cartesian plane (rectangular coordinate system) and label all the important features.
* Describe how to plot ordered pairs ( x, y ) in the coordinate plane.
TURN OVER
Ex) Draw a coordinate plane and plot the following ordered pairs.
( −1, 2 ) , ( 3, 4 ) , ( 0, 0 ) , ( 3, 0 ) , ( −2, − 3)
* Why is plotting ordered pairs on the coordinate plane beneficial?
Ex) The table shows the numbers N (in millions) of subscribers to a cellular telecommunication service in the United States from 2001 through 2010, where t represents the year. Sketch a scatter plot of the data. What appears to be the relationship between the two variables? Year, t
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Subscribers, N
128.4 140.8 158.7 182.1 207.9 233.0 255.4 270.3 290.9 311.0
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The Pythagorean Theorem and the Distance Formula * Use the Pythagorean Theorem to derive a formula that gives the distance between two points ( x1 , y1 ) and
( x2 , y2 ) in the coordinate plane.
Ex) Show that the points ( 2, 1) , ( 4, 0 ) , and
( 5, 7 )
are vertices of a right triangle.
TURN OVER
The Midpoint Formula * Use the distance formula to prove that the midpoint between two points ( x1 , y1 ) and ( x2 , y2 ) is given by:
x1 + x2 y1 + y2 , 2 2
See pg. 110
Ex) Find the midpoint of the line segment joining ( −5, − 3) and ( 9, 3) .
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Applications Ex) Draw a coordinate plane and a triangle with vertices at ( −1, 2 ) , (1, − 4 ) , and
( 2, 3) .
Then, shift the
triangle three units to the right and two units up and re-draw the triangle. What are the vertices of the shifted triangle? NOTE: The above shifts are called “TRANSLATIONS” and are considered “RIGID MOTIONS” since the size and shape of the triangle are unchanged (the triangles are congruent).
