Parallel and Perpendicular Lines

Tuesday, January 18thParallel and Perpendicular LinesModeling MathematicsMaterials:

Directions:Draw and cut out a scalene right triangle from the small square piece of graph paperLabel the triangle ABC where < C is the right angle. Label the sides of the triangle as shown

Modeling MathematicsDirections:Place triangle on coordinate plane where B lies on the origin and side a lies along the positive x-axis. Fill in the coordinates of B and slope of side c in the table under the TRIAL #1 column beside the Original Position rows

Rotate their triangles 90 counterclockwise so that B is still at the origin and side a is along the positive y-axis. Write the new coordinates of B and slope of side c in the table under the TRIAL #1 column beside the 90 counterclockwise rotation rows.

Now move the triangle down 2 units, to the right 3 units, and rotate the triangle 180 along point B. Write the new coordinates of B and slope of side c in the table under the TRIAL #1 column beside the 2 units down, 3 units right and 180 rotation rows.

Modeling Mathematics

Repeat this process TWO MORE TIMES, selecting a different starting place each time--i.e. not do not place B on (0,0)Write your answers under the TRIAL #2 and TRIAL #3 columns, respectively.

Place triangle on coordinate plane where B lies on the your selected location and side a lies along the positive x-axis. Fill in the coordinates of B and slope of side c in the table under the appropriate TRIAL column beside the Original Position rowsRotate their triangles 90 counterclockwise so that B is still at your selected location and side a is along the positive y-axis. Write the new coordinates of B and slope of side c in the table under the appropriate TRIAL column beside the 90 counterclockwise rotation rows.Now move the triangle down 2 units, to the right 3 units, and rotate the triangle 180 along point B. Write the new coordinates of B and slope of side c in the table under the appropriate TRIAL column beside the 2 units down, 3 units right and 180 rotation rows.

DefinitionsParallel LinesLines in the same plane that never intersect are called parallel.

If two non-vertical lines have the same slope, then they are parallel.and the converse is also trueIf two non-vertical lines are parallel, then they have the same slope.

Perpendicular LinesLines that intersect at right angles are called perpendicular lines

If the product of the slopes of two lines is -1, then the lines are perpendicular.and the converse is also trueIf two lines are perpendicular, then the product of the slopes is -1.

Example 1y = (1/4)x + 11y = 5x 82y 3x =2y + 4x = -6y = 5x + 1y = -3x + 2 Example 2Example 3What is the relationship (if any) between the two lines?Check for UnderstandingHold up the GREEN card if the lines or pairs of points are parallelHold up the RED card if the lines or pairs of points are perpendicularPARALLELorPERPENDICULAR

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Example 1x 3y = 8 2x 3y = 6 (5, -4) (-3, 2)Example 2Write an equation in slope-intercept form of the line that passes through the given point and is parallel to each equation.

Example 12x 9y = 5 y =(1/3)x + 2 (6, -13) (-3, 1)Example 2Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to each equation.

Putting it all togetherLines p, q, and r all pass through point (-3, 4). Line p has slope 4 and is perpendicular to line q. Line r passes through Quadrants I and II only.

(1) Write an equation for each line. (2) Graph the three lines on the same coordinate plane. HomeworkChapter 6.6 ExercisesPages 367-386Problems # 18, 20, 26, 30, 34, 38, 42, 44, 46, 48