Ch 6 – Coordinate Geometry. Recap – How do you calculate… …the length of a line segment? …the midpoint of two points? …the gradients of a line? …the y-intercept?

Slides:



Advertisements
Similar presentations
Co-Ordinate Geometry Maths Studies.
Advertisements

Geometry Mini-Lesson (1, −1) (−1, 1) (6, 3) (−6, −3)
What is a quadrilateral? -four sided polygon What is a parallelogram? A quadrilateral with - opposite sides parallel - opposite sides congruent - both.
C1: Parallel and Perpendicular Lines
10.2 Perpendicular Lines.
6.6 Warm-up Objective 3 The graph of which function is shown ?
The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal parts.
8.5 Use properties of kites and trapezoids
Term 3 : Unit 2 Coordinate Geometry
COORDINATE GEOMETRY Straight Lines The equations of straight lines come in two forms: 1.y = mx + c, where m is the gradient and c is the y-intercept. 2.ax.
Equation of Straight Line
Grade 11-Regular Coordinate Geometry Exercises Long Test #2 Coverage: Vertical Angles, Linear Pairs, Transversals, Parallel Lines, Coordinate Geometry.
Chin-Sung Lin. Mr. Chin-Sung Lin  Distance Formula  Midpoint Formula  Slope Formula  Parallel Lines  Perpendicular Lines.
Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.
C1: The Equation of a Straight Line, lesson 2
Coordinate Geometry Learning Outcomes
CO-ORDINATE GEOMETRY. DISTANCE BETWEEN TWO POINTS - Found by using Pythagoras In general points given are in the form (x 1, y 1 ), (x 2, y 2 ) (x 1, y.
COORDINATE GEOMETRY PROOFS USE OF FORMULAS TO PROVE STATEMENTS ARE TRUE/NOT TRUE: Distance: d= Midpoint: midpoint= ( ) Slope: m =
Co-ordinate Geometry. What are the equations of these lines. Write in the form ax + by + c = 0 1)Passes though (2,5) and gradient 6 2)Passes through (-3,2)
Trapezoids A quadrilateral with exactly one pair of parallel sides is called a trapezoid.
Proof using distance, midpoint, and slope
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 4 Use coordinate geometry SOLUTION One way is to show that a pair of sides are congruent and parallel. Then apply Theorem 8.9. First use the Distance.
Chapter 7 Coordinate Geometry 7.1 Midpoint of the Line Joining Two Points 7.2 Areas of Triangles and Quadrilaterals 7.3 Parallel and Non-Parallel Lines.
Jeopardy Angle Pairs Bisecting $100 $100 $100 $100 $100 $200 $200 $200
Using Coordinate Geometry to Prove Parallelograms
Aim: Slopes of Parallel Lines Course: Applied Geometry Do Now: a. y = 2x + 5 b. y = 2x – 1 c. y = 2x + 2 Aim: What is the relationship between slopes.
6.3 TESTS FOR PARALLELOGRAMS. If… Both pairs of opposite sides are parallel Both pairs of opposite sides are congruent Both pairs of opposite angles are.
COORDINATES, POINTS AND LINES S1/W2/HO-1/G.11/Math/RIT-AYA/ Name : _______________ Class : 10 ___ Day/date : _______________.
Unit 2 Test Review Geometry WED 1/22/2014. Pre-Assessment Answer the question on your own paper.
Proving Parallelograms: Coordinate Geometry Unit 1C3 Day 4.
Proving Quadrilaterals on the Coordinate Plane February 27, 2013.
Write Equations of Parallel and Perpendicular Lines
I can determine when lines are parallel and write equations of parallel lines.
Chapter 3 Section 1 Copyright © 2011 Pearson Education, Inc.
Parallel and Perpendicular Lines UNIT 2 REVIEW GEOMETRY.
Bell work: What geometric name(s) could you give each polygon? What properties/characteristics do you observe for each polygon?
Section 1-1 Points and Lines. Each point in the plane can be associated with an ordered pair of numbers, called the coordinates of the point. Each ordered.
Algebra – Linear Functions By the end of this lesson you will be able to identify and calculate the following: 1. Finding the equation of a straight line.
Warm-Up: Problem of the Day One endpoint of a line segment has coordinates (-3,- 1). The midpoint of the line segment is at (1,1). What is the location.
7.2 Parallelograms. Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. Consecutive angles Opposite angles.
Vectors – Ch 11. What do you know? The basics … A B 6 3 a or a Column vector –a–a Negative of a vector a A B A B.
A, B, and C lie on the same line. Work out k k = 2.
1.3 Distance & Midpoint I CAN FIND THE DISTANCE BETWEEN TWO POINTS AND THE MIDPOINT OF A SEGMENT.
8.5 Use Properties of Trapezoids and Kites Hubarth Geometry.
Coordinate Geometry Midpoint of the Line Joining Two Points Areas of Triangles Parallel and Non-Parallel Lines Perpendicular Lines.
Chapter 7 Coordinate Geometry 7.1 Midpoint of the Line Joining Two Points 7.2 Areas of Triangles and Quadrilaterals 7.3 Parallel and Non-Parallel Lines.
1-3 Use Midpoint and Distance Formulas Hubarth Geometry.
IB Studies Topic 5.1 and 6.2: straight line and linear models. 5.1 Gradient, equation of a line, parallel and perpendicular lines, points of intersection.
Warm Up.
Straight Line Graph revision
Aim: How can we solve coordinate quadrilateral proofs
Straight Line Graph revision
EXAMPLE 4 Use coordinate geometry
Using Coordinate Geometry to Prove Parallelograms
Lesson 8.3: Show that a Quadrilateral is a Parallelogram
Quadrilaterals and Coordinates Proof
Using Coordinate Geometry to Prove Parallelograms
Lesson 5-4 Coordinate Geometry
Section 1 – Introduction to Analytic Geometry
MODULE - 9 QUADRILATERALS
6-2 & 6-3: Parallelograms Rigor: Use properties of parallelograms to solve equations and prove a given quadrilateral is a parallelogram. Relevance –
Warm-up Write the equation of the line:
DRILL
Lesson: 6.6 Trapezoids Objectives:
Review Unit 6 Test 1.
Geometry Section  I can use the properties of parallelograms to set up and solve equations to find variables.
Gradient of a line Recap
Further Coordinate Geometry
Parallel and Perpendicular Lines
Presentation transcript:

Ch 6 – Coordinate Geometry

Recap – How do you calculate… …the length of a line segment? …the midpoint of two points? …the gradients of a line? …the y-intercept?

Recap

Example 1 P is the point (3, 8). Q is the point (-1, 5). i.Find the equation of PQ. ii.Find the equation of the line parallel to PQ which passes through the point (2, -3)

Worksheets – in pairs Sheet 1 – Exercise 1 Sheet 2 – Using the information on card A – answer card B to L

Textbook Questions For further practice, look through Ex1A-1D

Example A quadrilateral ABCD has vertices at A(0,-4), B(-2,2), C(3,4) and D(5,2). Calculate the area of ABCD.

Worksheets – in pairs Exercises 2&3

Textbook Questions p23 – Misc Ex 1 – Q1,4,7,14-17,23-25 This needs to be completed and marked by Friday (answers in the back of the book).