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3.8 Analyzing Polygons with Coordinates

. 3.8 Analyzing Polygons with Coordinates Essential Question: How can we properly identify parallel and perpendicular lines in the coordinate plane using the definition of slope? BE LLRINGER

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3.8 Analyzing Polygons with Coordinates

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  1. . 3.8 Analyzing Polygons with Coordinates Essential Question: How can we properly identify parallel and perpendicular lines in the coordinate plane using the definition of slope? BELLRINGER To go from ( -3 , 2) to ( 9 , 7 ) in a coordinate plane, you must move how many units to the right? and how many units up? *TWO PART QUESTION* Slope Rida

  2. Definition of Slope The slope of a nonvertical line that contains the points (x1 , y1) and (x2 , y2) is eqaul to the ratio y2 - y1 x2 - x1 Guided Practice *Use the definition of slope formula to find the slope of the line* 1.) A ( 5 , 3 ) B ( 2 , 3) 2.) A ( 0 , 0 ) B ( 4 , 4 ) 3.) A ( 5 , 2 ) B ( 3 , 8 )

  3. You try... Use the definition of slope formula to find the slope of the following points 1.) A ( 3 , 1 ) B ( -1 , 3 ) 2.) A ( 0 , 0 ) B ( 4 , 2 ) 3.) A ( 1 , 3 ) B ( 5 , 2 )

  4. Parallel Lines Theorem In a coordinate plane, two nonvertical lines are parallel if and only if they have the SAME slope. Any two vertical lines are parallel. Perpendicular Lines Theorem In a coordinate plane, two nonvertical lines are perpendicular if and only if the product of their slopes is - 1. Any vertical line is perpendicular to any horizontal line.

  5. Recognizing Parallel and Perpendicular Lines by Coordinates 1.) Plot the points of the following line segments 2.) Find the slope of each line segment 3.) Determine if they are parallel , perpendicular , or neither. 1.) A ( -1 , 1) and B ( 2 , 3 ) ; C ( 2 , 2 ) and D ( 5 , 4 ) 2.) A ( -2 ,1 ) and B ( 1 , -2 ) ; C ( -1 , -1 ) and D ( 3 , 3 ) 3.) A ( -1 , 2 ) and B ( 1 , -2 ) ; C ( 1 , -2 ) and D ( 2 , -1 )

  6. 1.Find the slope of SA. 2. Find the slope of TB. 3. Is 1 a right angle? Explain your answer.

  7. EXIT TICKET Find the slope of the following two line segments. A ( 1 , 5 ) and B ( 3 , 9 ) ; C ( -1 , 6 ) and D ( -4 , 0 ) Are the two line segments parallel, perpendicular, or neither? Explain how you know the line segments are either parallel, perpendicular, or neither?

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