C1: Chapter 5 Coordinate Geometry

Dr J Frost (jfrost@tiffin.kingston.sch.uk)

Last modified: 30th September 2013

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6

y4

3

2

1

-1

-2

-3

-4

A

B

C

D

E

F

G

H

x -5 -4 -3 -2 -1 0 1 2 3 4 5 6

y4

3

2

1

-1

-2

-3

-4

How would we draw

This becomes:

Revision

What is the gradient and y-intercept of the line ?Gradient y-intercept

What is the gradient and y-intercept of the line ?Gradient y-intercept

A line is parallel to the line and passes through the point . Work out the equation of the line.

The line meets the -axis at the point . Work out the coordinates of .

The line meets the -axis at the point . Work out the coordinates of .

A line is parallel to the line and it passes through the point . Write down the equation of the line.

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1

2

3

4

5

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Equation of a line given a point and gradient

x

y

(𝑥1 , 𝑦 1 )

𝑦− 𝑦1=𝑚 (𝑥−𝑥1 )This is one and only formula you need this

chapter, and you MUST remember it.

Where do you think this comes from?

!

Gradient using two points

Point 1 Point 1 Gradient(0,0) (2,6) 3

(1,3) (3,7) 2

(0,5) (4,25) 5

(2,2) (-1,5) -1

Q1

Q2

Q3

Q4

(4,3) (10,6) 0.5Q5

(7,8) (-4,-3) 1Q6

(7,1) (-1,5) -0.5Q7

(6,5) (8,1) -2Q8

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In general:

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Quickfire Examples

Point 1 Gradient Unsimplified Equation(3,4) 2 𝑦−4=2 (𝑥−3 )(-5,0) -1 𝑦=−1 (𝑥+5 )(1,-3) 4 𝑦+3=4 (𝑥−1 )(4,7) 3 𝑦−7=3 (𝑥−4 )

Q1

Q2

Q3

Q4

(-3,-2) 5 𝑦+2=5 (𝑥+3)Q5

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𝑦− 𝑦1=𝑚 (𝑥−𝑥1 )

Examples

𝑦− 𝑦1=𝑚 (𝑥−𝑥1 )

Find the equation of the line with gradient that passes through the point . Put your equation in the form .

The line meets the -axis at the point . Find the equation of the line with gradient and passes through the point . Write your answer in the form where are integers.

The lines and intersect at the point . The point has coordinates . Find the equation of the line that passes through the points and . Write your answer in the form where are integers.

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Q1

Q2

Q3

Perpendicular Lines

If two lines, with gradients and , are perpendicular, what can we say about the relationship between and ?

Gradient Gradient of Perpendicular Line

2 -1/2

-3 1/3

1/4 -4

5 -1/5

-2/7 7/2

7/5 -5/7

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Example Problems

A line is goes through the point (9,10) and is perpendicular to another line with equation . What is the equation of the line?

A line goes through the points and . A second line is perpendicular to and passes through point B. Where does cross the x-axis?

Are the following lines parallel, perpendicular, or neither?

Neither. Gradients are and . But , not -1, so not perpendicular.

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Q1

Q2

Q3

Checking your understandingEdexcel May 2013 (Retracted)

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Checking your understandingEdexcel Jan 2013

a) b) c)

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Exercises

C1 Page 78 (Old Textbook)Mixed Exercise 5FQ1 onwards.