Distance between two points

Slides:

Advertisements

Similar presentations

Proving the Distance Formula

Advertisements

The Distance Formula Lesson 9.5.

Taxicab Geometry. Uses a graph and the movement of a taxi Uses the legs of the resulting right triangle to find slope, distance, and midpoint.

10.7 Write and Graph Equations of Circles Hubarth Geometry.

GeometryGeometry Lesson 75 Writing the Equation of Circles.

1-7: Midpoint and Distance in the Coordinate Plane

Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA

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.

8-1, 1-8 Pythagorean Theorem, Distance Formula, Midpoint Formula

Midpoint and Distance Formulas Section 1.3. Definition O The midpoint of a segment is the point that divides the segment into two congruent segments.

Chapter 1, Section 6. Finding the Coordinates of a Midpoint  Midpoint Formula: M( (x1+x2)/2, (y1+y2)/2 )  Endpoints (-3,-2) and (3,4)

6-3 Warm Up Problem of the Day Lesson Presentation

Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

Lesson 6-4 Example Example 3 Determine if the triangle is a right triangle using Pythagorean Theorem. 1.Determine which side is the largest.

6-3 The Pythagorean Theorem Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

Lesson 1-2 Section 1-4. Postulate Definition Example 1.

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.

Applying the Pythagorean Theorem and Its Converse Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson.

GeometryGeometry 10.6 Equations of Circles Geometry.

3.4 Is It A Right Triangle? Pg. 13 Pythagorean Theorem Converse and Distance.

13.1 The Distance and Midpoint Formulas. Review of Graphs.

Finding the distance between two points. (-4,4) (4,-6)

Topic 5-1 Midpoint and Distance in the Coordinate plan.

TOOLS OF GEOMETRY UNIT 1. TOOLS OF GEOMETRY Date Essential Question How is the Pythagorean Theorem used to find the distance between two points? Home.

1. Factor 2. Factor 3.What would the value of c that makes a perfect square. Then write as a perfect square. M3U8D3 Warm Up (x+4) 2 (x-7) 2 c = 36 (x+6)

Pre-Calculus Coordinate System. Formulas  Copy the following formulas into your notes. –Distance Formula for Coordinate Plane –Midpoint Formula for Coordinate.

Area & Perimeter on the Coordinate Plane

Equations of Circles. Vocab Review: Circle The set of all points a fixed distance r from a point (h, k), where r is the radius of the circle and the point.

 Then: You graphed points on the coordinate plane.  Now: 1. Find the distance between points. 2. Find the midpoint of a segment.

How can you prove the Pythagorean Theorem by using the diagram below?

Pythagorean Theorem & Distance Formula Anatomy of a right triangle The hypotenuse of a right triangle is the longest side. It is opposite the right angle.

Algebra 1 Predicting Patterns & Examining Experiments Unit 5: Changing on a Plane Section 2: Get to the Point.

Using the Distance Formula in Coordinate Geometry Proofs.

Distance on a coordinate plane. a b c e f g d h Alternate Interior angles Alternate exterior angles corresponding angles supplementary angles.

Applying the Pythagorean Theorem and Its Converse 3-9 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson.

Midpoint and distance formulas

Beat the Computer Drill Equation of Circle

Midpoint And Distance in the Coordinate Plane

1-7: Midpoint and Distance in the Coordinate Plane

Right Triangle The sides that form the right angle are called the legs. The side opposite the right angle is called the hypotenuse.

Copyright © Cengage Learning. All rights reserved.

Evaluate each expression.

Midpoint And Distance in the Coordinate Plane

Lesson 2.7 Core Focus on Geometry The Distance Formula.

Equations of Circles.

Section 1.1 – Interval Notation

Distance on the Coordinate Plane

Pythagorean Theorem and Distance

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Algebra 1 – The Distance Formula

Chapter 1: Lesson 1.1 Rectangular Coordinates

Math Humor Q: What keeps a square from moving?.

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

6-3 Warm Up Problem of the Day Lesson Presentation

The Distance Formula Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates;

Unit 5: Geometric and Algebraic Connections

Unit 3: Coordinate Geometry

Chapter 9 Section 8: Equations of Circles.

Objectives Write equations and graph circles in the coordinate plane.

The Distance Formula Lesson 9.5.

Comprehensive Test Friday

1.7 Midpoint and Distance in the Coordinate Plane

Triangle Relationships

Warm-up (YOU NEED A CALCLULATOR FOR THIS UNIT!)

The Distance Formula Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates;

Presentation transcript:

Distance between two points Unit 5 Lesson 1 Distance between two points

How do we find the distance between two points? Suppose we are asked to find the distance between the points C(1, 3) and D(-2, 4). How would we begin to find the distance?

1. Let’s graph the points on a coordinate plane so we can visualize the distance between these points

Notice how we created a right triangle. 2. Now let’s draw a path from one point to the next point in the shape of a triangle. Notice how we created a right triangle.

3. Since we now have a right triangle, we can use the Pythagorean theorem to find the distance between the points. The Pythagorean Theorem: a2 + b2 = c2 For our problem, a = 1, b = 3 and c is the unknown. Substituting into the formula… (1)2 + (3)2 = c2 1 + 9 = c2 10 = c2 = c 1 3

Distance Formula Using the Pythagorean Theorem, we can create a formula that will allow us to find the distance between two points. Using the points:

Our problem revisited using the distance formula…. Suppose we are asked to find the distance between the points C(1, 3) and D(-2, 4). Substituting into the distance formula….

Conclusions We can use the Pythagorean Theorem to find distances between points. We can also use the distance formula to find distances between points.