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# Coordinate Geometry

Rate of change and slope

by

Tweet## Linda Bennett

on 7 November 2012#### Transcript of Coordinate Geometry

Rate of Change and Slope Coordinate Geometry Geometry Rate of Change Slope Ratio of the amount of

change in the output to

the amount of change in the input. Is all around us! Rectangles Rectangles Circles Squares Day 1 Day 2 Day 3 Day 4 Day 5 Lawns Mowed Amount Earned ($) 1 3 6 8 13 15 45 90 120 195 Day 1 to Day 2 change in $ change in lawns = 45 - 15 3 - 1 = 30 2 = 15 Day 2 to Day 3 change in $ change in lawns = 90 - 45 6 - 3 = 45 3 = 15 Day 3 to Day 4 change in $ change in lawns = 120 - 90 8 - 6 = 30 2 = 15 Day 4 to Day 5 change in $ change in lawns = 195 - 120 13 - 8 = 75 5 = 15 Positive slope Negative Slope Triangles Slope a number that describes the steepness of a line = vertical change horizontal change = rise run rise run Horizontal Lines have no slope. The slope of a vertical line is undefined. Slope = 0 Haven't had enough fun with slope?

Go to http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/Rate.htm Show whether opposite sides are parallel and whether adjacent sides are perpendicular.

Is the figure a rectangle?

2/3 = 2/3, so opposite sides are parallel;

-3/2 x 2/3 = -1, so adjacent sides are perpendicular.

The figure is a rectangle. Solve Make a Plan 2. Write parallel or perpendicular to make the statement true.

If opposite sides of a quadrilateral are _parallel______ and adjacent sides are _perpendicular_ , the quadrilateral is a rectangle. Make a Plan 1. What properties make a quadrilateral a rectangle? Understand the Problem The four points listed below are the coordinates of the vertices of quadrilateral ABCD.

Use slope to decide whether the quadrilateral is a rectangle.

A(-4, -3) B(2, 1) C(4, -2) D(-2, -6) Holt Middle School Mathematics Course 3 , Copyright 2005, Holt, Rinehart and Winston

Houghton Mifflin Harcourt- On Core , Mathematics Middle School Grade 8, Copyright 2010

www.youtube.com, Geometry in Real Life by Mark Carl, music by John Mayer

www.regentsprep.org , Algebra Lesson Page, Slope and Rate of Change Additional Resources: This prezi was created by:

Linda Bennett

8th Grade Math

Ponchatoula Jr. High Prezi-tation Credits: Plot and connect the 4 vertices to see if quadrilateral ABCD looks like a rectangle. Check Find the slope of AB, BC, CD, and AD. Solve How can you calculate the slope of a line if you know the coordinates of 2 points?

Sample answers: divide rise by run;

Slope = vertical change

horizontal change Make a Plan Write parallel or perpendicular to make the statement true.

If opposite sides of a quadrilateral are _____________ and adjacent sides are _____________ , the quadrilateral is a rectangle. Make a Plan A. XY SLOPE

OF A

LINE Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry D. DM Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry C. BC Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry B. ZA Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry slope of DM = 0 D. DM Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry slope of BC is undefined C. BC Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry 1

2 –1

2 negative slope;

slope of ZA = = – B. ZA Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry 5

4 –5

–4 positive slope;

slope of XY = = A. XY Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry D. DM slope of DM = 0 How can slope show that two lines are parallel or perpendicular? 1. Two lines in a plane that never meet are called ________________ lines.

2. ______________ lines intersect at right angles.

3. The symbol || means that lines are ____________ .

4. When a transversal intersects two ___________ lines, all of the acute angles are congruent. 1. Two lines in a plane that never meet are called parallel lines. 2. Perpendicular lines intersect at right angles. 3. The symbol || means that lines

are parallel. 4. When a transversal intersects two parallel lines, all of the acute angles are congruent. 2/3, - 3/2, 2/3, - 3/2, Opposite sides are parallel and congruent. Adjacent sides are perpendicular. If their slopes are equal, the lines are parallel. If the product of their slopes is -1, the lines are perpendicular.

Full transcriptchange in the output to

the amount of change in the input. Is all around us! Rectangles Rectangles Circles Squares Day 1 Day 2 Day 3 Day 4 Day 5 Lawns Mowed Amount Earned ($) 1 3 6 8 13 15 45 90 120 195 Day 1 to Day 2 change in $ change in lawns = 45 - 15 3 - 1 = 30 2 = 15 Day 2 to Day 3 change in $ change in lawns = 90 - 45 6 - 3 = 45 3 = 15 Day 3 to Day 4 change in $ change in lawns = 120 - 90 8 - 6 = 30 2 = 15 Day 4 to Day 5 change in $ change in lawns = 195 - 120 13 - 8 = 75 5 = 15 Positive slope Negative Slope Triangles Slope a number that describes the steepness of a line = vertical change horizontal change = rise run rise run Horizontal Lines have no slope. The slope of a vertical line is undefined. Slope = 0 Haven't had enough fun with slope?

Go to http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/Rate.htm Show whether opposite sides are parallel and whether adjacent sides are perpendicular.

Is the figure a rectangle?

2/3 = 2/3, so opposite sides are parallel;

-3/2 x 2/3 = -1, so adjacent sides are perpendicular.

The figure is a rectangle. Solve Make a Plan 2. Write parallel or perpendicular to make the statement true.

If opposite sides of a quadrilateral are _parallel______ and adjacent sides are _perpendicular_ , the quadrilateral is a rectangle. Make a Plan 1. What properties make a quadrilateral a rectangle? Understand the Problem The four points listed below are the coordinates of the vertices of quadrilateral ABCD.

Use slope to decide whether the quadrilateral is a rectangle.

A(-4, -3) B(2, 1) C(4, -2) D(-2, -6) Holt Middle School Mathematics Course 3 , Copyright 2005, Holt, Rinehart and Winston

Houghton Mifflin Harcourt- On Core , Mathematics Middle School Grade 8, Copyright 2010

www.youtube.com, Geometry in Real Life by Mark Carl, music by John Mayer

www.regentsprep.org , Algebra Lesson Page, Slope and Rate of Change Additional Resources: This prezi was created by:

Linda Bennett

8th Grade Math

Ponchatoula Jr. High Prezi-tation Credits: Plot and connect the 4 vertices to see if quadrilateral ABCD looks like a rectangle. Check Find the slope of AB, BC, CD, and AD. Solve How can you calculate the slope of a line if you know the coordinates of 2 points?

Sample answers: divide rise by run;

Slope = vertical change

horizontal change Make a Plan Write parallel or perpendicular to make the statement true.

If opposite sides of a quadrilateral are _____________ and adjacent sides are _____________ , the quadrilateral is a rectangle. Make a Plan A. XY SLOPE

OF A

LINE Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry D. DM Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry C. BC Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry B. ZA Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry slope of DM = 0 D. DM Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry slope of BC is undefined C. BC Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry 1

2 –1

2 negative slope;

slope of ZA = = – B. ZA Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry 5

4 –5

–4 positive slope;

slope of XY = = A. XY Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line. Finding the Slope of a Line Coordinate Geometry D. DM slope of DM = 0 How can slope show that two lines are parallel or perpendicular? 1. Two lines in a plane that never meet are called ________________ lines.

2. ______________ lines intersect at right angles.

3. The symbol || means that lines are ____________ .

4. When a transversal intersects two ___________ lines, all of the acute angles are congruent. 1. Two lines in a plane that never meet are called parallel lines. 2. Perpendicular lines intersect at right angles. 3. The symbol || means that lines

are parallel. 4. When a transversal intersects two parallel lines, all of the acute angles are congruent. 2/3, - 3/2, 2/3, - 3/2, Opposite sides are parallel and congruent. Adjacent sides are perpendicular. If their slopes are equal, the lines are parallel. If the product of their slopes is -1, the lines are perpendicular.