Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel.

Slides:

Advertisements

Similar presentations

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–5) CCSS Then/Now New Vocabulary Key Concept: Distance Between a Point and a Line Postulate.

Advertisements

Equations of parallel, perpendicular lines and perpendicular bisectors

Parallel & Perpendicular Lines

Parallel & Perpendicular Lines Parallel Lines m = 2/1 What is the slope of the 2 nd line?

7.8 Parallel and Perpendicular Lines Standard 8.0: Understand the concepts of parallel and perpendicular lines and how their slopes are related.

Slope of Parallel and Perpendicular Lines Geometry 17.0 – Students prove theorems by using coordinate geometry, including various forms of equations of.

Unit 1 Basics of Geometry Linear Functions.

Parallel & Perpendicular Lines. Parallel and Perpendicular Lines The two lines shown below are parallel (never intersect). Identify the slope of each.

Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio Send all.

1.4: equations of lines CCSS:

Using properties of Midsegments Suppose you are given only the three midpoints of the sides of a triangle. Is it possible to draw the original triangle?

5.7 Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

10.2 Perpendicular Lines.

Warm Up Solve each equation for y. 1. y – 6x = 92. 4x – 2y = 8 2.9A Parallel and Perpendicular Lines.

Writing equations given slope and point

CONCEPT: WRITING EQUATIONS OF LINES EQ: HOW DO WE WRITE THE EQUATION OF A LINE THAT IS PARALLEL OR PERPENDICULAR TO A GIVEN LINE? (G.GPE.5) VOCABULARY.

Equations of lines.

Introduction The slopes of parallel lines are always equal, whereas the slopes of perpendicular lines are always opposite reciprocals. It is important.

3-3 Slopes of Lines You used the properties of parallel lines to determine congruent angles. Find slopes of lines. Use slope to identify parallel and perpendicular.

5.1 Bisectors, Medians, and Altitudes. Objectives Identify and use ┴ bisectors and  bisectors in ∆s Identify and use medians and altitudes in ∆s.

Standardized Test Practice:

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–5) CCSS Then/Now New Vocabulary Key Concept: Distance Between a Point and a Line Postulate.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–3) CCSS Then/Now New Vocabulary Key Concept: Nonvertical Line Equations Example 1:Slope and.

Writing Equations of Lines. Do Now: Answer each of the following questions based on the graph 1.What is the slope of the line? 2.What is the y-intercept?

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–3) CCSS Then/Now New Vocabulary Key Concept:Slope-Intercept Form Example 1:Write an Equation.

Point-Slope Formula Writing an Equation of a line Using the Point-Slope Formula.

Writing & Identifying Equations of Parallel & Perpendicular Lines Day 94 Learning Target: Students can prove the slope criteria for parallel and perpendicular.

Everything You Will Ever Need To Know About Linear Equations*

Finding Equations of Lines If you know the slope and one point on a line you can use the point-slope form of a line to find the equation. If you know the.

Chapter 7 Determine the Relationship of a System of Equations 1/4/2009 Algebra 2 (DM)

2.5 Writing Equation of a Line Part 2 September 21, 2012.

You found the slopes of lines.

Warm Up Given: (3, -5) and (-2, 1) on a line. Find each of the following: 1.Slope of the line 2.Point-Slope equation of the line 3.Slope-Intercept equation.

 Perpendicular Bisector- a line, segment, or ray that passes through the midpoint of the side and is perpendicular to that side  Theorem 5.1  Any point.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–3) Then/Now New Vocabulary Key Concept:Slope-Intercept Form Example 1:Write an Equation in.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–5) NGSSS Then/Now New Vocabulary Key Concept: Distance Between a Point and a Line Postulate.

GEOMETRY HELP Find and compare the slopes of the lines. Each line has slope –1. The y-intercepts are 3 and –7. The lines have the same slope and different.

5-6 PARALLEL AND PERPENDICULAR LINES. Graph and on the same coordinate plane. Parallel Lines: lines in the same plane that never intersect Non-vertical.

Distance, Slope, & Linear Equations. Distance Formula.

Section P.2 – Linear Models and Rates of Change. Slope Formula The slope of the line through the points (x 1, y 1 ) and (x 2, y 2 ) is given by:

Parallel & Perpendicular Lines

Warm up Recall the slope formula:

Algebra Parallel lines have the same ___________ but different _______________. slope y-intercepts Determine whether the graphs of each pair of.

Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc.,

Perpendiculars and Distance Page 215 You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find.

Medians, and Altitudes.

Five-Minute Check (over Lesson 1–3) Mathematical Practices Then/Now

OBJECTIVE I will use slope-intercept form to write an equation of a line.

Lesson 3-6: Perpendicular & Distance

Parallel and Perpendicular Lines

Perpendiculars and Distance

Parallel Lines: SLOPES ARE THE SAME!!

PARALLEL LINES Graphs: Lines Never Intersect and are in the same plane

Medians and Altitudes Median – A segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex. Centroid – The point.

Introduction The slopes of parallel lines are always equal, whereas the slopes of perpendicular lines are always opposite reciprocals. It is important.

Perpendiculars and Distance

9.3 Graph and Write Equations of Circles

PARALLEL LINES Graphs: Lines Never Intersect and are in the same plane

Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints P(5, 2) and Q(1, –4). Step 1 Graph PQ. The perpendicular.

Warm up Write an equation given the following information.

Warm up Write an equation given the following info:

PERPENDICULAR LINES.

Mathematical Practices

Five-Minute Check (over Lesson 2–7) Mathematical Practices Then/Now

Presentation transcript:

Then/Now You proved that two lines are parallel using angle relationships. Find the distance between a point and a line. Find the distance between parallel lines.

Vocabulary equidistant

Concept

Example 3 Distance Between Parallel Lines Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x – 1, respectively. You will need to solve a system of equations to find the endpoints of a segment that is perpendicular to both a and b. From their equations, we know that the slope of line a and line b is 2. Sketch line p through the y-intercept of line b, (0, –1), perpendicular to lines a and b. a b p

Example 3 Distance Between Parallel Lines Step 1 Use the y-intercept of line b, (0, –1), as one of the endpoints of the perpendicular segment. Write an equation for line p. The slope of p is the opposite reciprocal of Point-slope form Simplify. Subtract 1 from each side.

Example 3 Distance Between Parallel Lines Use a system of equations to determine the point of intersection of the lines a and p. Step 2 Substitute 2x + 3 for y in the second equation. Group like terms on each side.

Example 3 Distance Between Parallel Lines Simplify on each side. Multiply each side by. Substitutefor x in the equation for p.

Example 3 Distance Between Parallel Lines Simplify. The point of intersection is or (–1.6, –0.2).

Example 3 Distance Between Parallel Lines Use the Distance Formula to determine the distance between (0, –1) and (–1.6, –0.2). Step 3 Distance Formula x 2 = –1.6, x 1 = 0, y 2 = –0.2, y 1 = –1 Answer: The distance between the lines is about 1.79 units.

Example 3 A.2.13 units B.3.16 units C.2.85 units D.3 units Find the distance between the parallel lines a and b whose equations are and, respectively.