Slope and Midpoint.

Slides:

Advertisements

Similar presentations

Warm up Tell whether the relation is a function.

Advertisements

Apply the Distance & Midpoint formulas Find the distance and the midpoint Find the missing endpoint.

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?

10.2 Perpendicular Lines.

Lesson 1-3: Use Distance and Midpoint Formulas

The Midpoint Formula. The purpose of the midpoint formula The midpoint formula is used to find the midpoint or the halfway point of a line segment or.

Vocabulary The distance between any two points (x 1, y 1 ) and (x 2, y 2 ) is Distance Formula 9.6Apply the Distance/Midpoint The midpoint of a line segment.

In the skateboard design, VW bisects XY at point T, and XT = 39.9 cm. Find XY. Skateboard SOLUTION EXAMPLE 1 Find segment lengths Point T is the midpoint.

Proving the Midsegment of a Triangle Adapted from Walch Education.

The Distance and Midpoint Formulas Goal 1 Find the Midpoint of a Segment Goal 2 Find the distance between two points on a coordinate plane Goal 3 Find.

Distance and Midpoints

There’s a quiz on the table. Please take one and get started.

Chapter 1.3 Notes: Use Midpoint and Distance Formulas Goal: You will find lengths of segments in the coordinate plane.

Perpendicular Bisector of a Line To find the equation of the perpendicular bisector of a line segment : 1. Find the midpoint 2. Find the slope of the given.

Holt Geometry 1-6 Midpoint and Distance in the Coordinate Plane Develop and apply the formula for midpoint. Use the Distance Formula to find the distance.

Midpoint and Distance Formulas Goal 1 Find the Midpoint of a Segment Goal 2 Find the Distance Between Two Points on a Coordinate Plane 12.6.

Warm Up:. What is Geometry?  A branch of mathematics that studies the shape and size of objects.

Finding the Distance Between Two Points. Distance Formula Where does this formula come from and how do we use it? Consider the following example….

EXAMPLE 3 Use the Midpoint Formula a. FIND MIDPOINT The endpoints of RS are R(1,–3) and S(4, 2). Find the coordinates of the midpoint M.

Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up.

Polygons in the Coordinate Plane Techniques Examples Practice Problems.

Aim: Review the distance and midpoint Do Now: in the triangle, find the lengths of two legs (-2,4) (3,6) (3,4)

12.4 The Distance Formula Objectives: Use the distance formula to find the distance between 2 points in a coordinate plane. Determine whether a triangle.

3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz

1.8 Midpoint & Distance Formula in the Coordinate Plane Objective: Develop and apply the formula for midpoint. Use the Distance Formula and the Pythagorean.

Holt McDougal Geometry 3-5 Slopes of Lines Toolbox Pg. 185 (10-16 even; 19-22; 27 why 4 ; 38-40)

Unit 2-2 Slope. What is slope? The _________ of a line in a coordinate plane is a number that describes the steepness of the line. Any ____ points on.

Slope & Midpoint on the Coordinate Plane. SLOPE FORMULA Given two points (x 1,y 1 ) and (x 2,y 2 ) SLOPE The rate of change to get from one point to another.

Sec. 1 – 8 The Coordinate Plane Objectives: 1) Find the distance between 2 points on the coordinate plane. 2) Find the coordinate of the midpoint of a.

Equation of Circle Midpoint and Endpoint Distance Slope

1.3 Distance & Midpoint I CAN FIND THE DISTANCE BETWEEN TWO POINTS AND THE MIDPOINT OF A SEGMENT.

3-5 Slopes of Lines Warm Up Lesson Presentation Lesson Quiz

Objectives Develop and apply the formula for midpoint.

The coordinate plane is formed by the intersection of two perpendicular number lines called axes. The point of intersection, called the origin, is at 0.

Daily Review 1.) Find the measurement of PQ

Midpoint and Distance Formulas

Section 1.7 Midpoint and Distance in the Coordinate Plane

Midpoint and Distance Formulas

Warm up Tell whether the relation is a function. {(-1, 5), (-3, 2), (2, 0), (1, 2)} Evaluate: f(x) = 2x2 – 4 when x = -3 Find the slope: (5,

1.5 Writing Equations of Parallel and Perpendicular Lines

Apply the Distance & Midpoint formulas

Lesson 1-3 Formulas Lesson 1-3: Formulas.

Distance and Midpoints

Distance and Midpoint Formulas

2.2.4 Use slope criteria for parallel and perpendicular lines to solve problems on the coordinate plane.

1-7: Midpoint and Distance in the Coordinate Plane

Midpoint and Distance in the Coordinate Plane

Parallel and Perpendicular Lines

Topic: Slopes of Lines Section: 3-3 Concept.

Parallel Lines: SLOPES ARE THE SAME!!

Objectives Develop and apply the formula for midpoint.

Apply the Distance/Midpoint

Do Now Tell whether these two lines are parallel, perpendicular or neither. Given the ordered pair, (-1, 4), write an equation in point-slope form that.

Objectives Find the slope of a line.

3.4 Proofs with perpendicular lines

Warm up Tell whether the relation is a function.

Warm up Tell whether the relation is a function.

13.1 Cooridinate Geometry.

Warm up Tell whether the relation is a function.

Distance Formula Essential Question: How do we find the distance between two coordinate points? Demonstrated by using the distance formula in the notes.

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 Tell whether the relation is a function. {(-1, 5), (-3, 2), (2, 0), (1, 2)} Evaluate: f(x) = 2x2 – 4 when x = -3 Find the slope:

Review Unit 6 Test 1.

Equations of Lines.

Unit 1 Test Review.

3-6 Warm Up Find the value of m

Warm up Tell whether the relation is a function.

1.3 Use Midpoint and Distance Formulas

Writing the equation of the

Presentation transcript:

Slope and Midpoint

Recall: What is slope (again)? SLOPE FORMULA:

Example Find the slope of the line that contains the following points (6, -3) and (-10,5). -Substitute into slope formula: 5 - -3 6 - -10 -Simplify: 5 + 3 = 8 = 1 6 + 10 = 16 2

Example The lines are PARALLEL. Tell whether the lines through the given points are parallel, perpendicular, or neither. Line A: (3,-6) and (-4,8) Line B: (0,2) and (-1,4) Line A: 8 - -6 = 8 +6 = 14 -4 -3 = -4-3 = -7 Slope is -2 Line B: 4 – 2 = 2 -1– 0 = -1 Slope is -2 The lines are PARALLEL.

Example B. Line A: (-1,0) and (6,5) Line B: (-7,-8) and (4,0) Line A: 5 – 0 = 5 6- -1 = 7 Slope is 5/7 Line B: 0- -8 = 8 4- -7 = 11 Slope is 8/11 Lines are NEITHER parallel or perpendicular.

Example C. Line A: (5,9) and (10,11) Line B: (1,8) and (3,3) Line A: 11 – 9 = 2 10 – 5 = 5 Slope of 2/5 Line B: 3- 8 = -5 3- 1 = 2 Slope is -5/2 Lines are PERPENDICULAR.

What is the midpoint of a segment? The midpoint of a segment is the point located exactly halfway between the two endpoints. The midpoint of a segment is the halfway point. A M B

Example In the diagram, M is the midpoint of the segment. Find the value of x, MQ, and PQ. Q P M 4x - 1 12x - 17 4x -1 = 12x - 17 MQ = 12(2) -17 24 – 17 PM = 4(2) -1 8 – 1 -12x -12x -8x – 1 =-17 PM = 7 MQ = 7 +1 +1 -8x = -16 x = 2

Midpoint Formula Given the location of the two endpoints, you need the midpoint formula.

Example Find the coordinates of the midpoint of the segment with the given endpoints. CD, where C(-2,-1) and D(4,2) ( -2 + 4 , -1 + 4) 2 2 ( 2 , 3 ) 2 2 Midpoint = (1, 3/2)

Example B. EF, where E(-2,3) and F(5, -3) ( -2 + 5 , 3 + -3) 2 2 ( -2 + 5 , 3 + -3) 2 2 ( 3 , 0 ) 2 2 Midpoint = (3/2, 0)

What if you are given an endpoint and the midpoint, and are asked to find the other endpoint? Ex: Use the given endpoint R and the midpoint M of RS to find the coordinates of the other endpoint S. R(8,0) and M(4,-5) R (8,0) M (4,-5) S ( , ) -10 -4 -5 -4 -5

Example Ex: Use the given endpoint R and the midpoint M of RS to find the coordinates of the other endpoint S. R(-8,3) and M(-2,7) R (-8,3) M (-2,7) S ( , ) 4 11 +6 +4 +6 +4