C1: Chapter 5 Coordinate Geometry Dr J Frost ([email protected]) Last modified: 30 th September 2013
Dec 22, 2015
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.
? ?
? ?
?
?
?
?
1
2
3
4
5
6
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
? ? ? ? ? ? ? ?
In general:
?
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
? ? ? ? ?
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.
?
?
?
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
? ? ? ? ? ?
?
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.
?
?
?
Q1
Q2
Q3