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Perpendicular lines

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by

Mr Mattock

on 20 May 2017

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Transcript of Perpendicular lines

Perpendicular lines
L.O. - Understand the relationship between perpendicular lines.
Perpendicular Lines
The red and green line
meet at right angles.

What do we notice
about their gradients?
Perpendicular Lines
The red and green line
meet at right angles.

What do we notice
about their gradients?

One is and one is -
2
3
3
2
Perpendicular Lines
Lines that are perpendicular have gradients that are the negative reciprocal of each other; i.e. if one line
has a gradient of then the perpendicular line will have a gradient of - .
3
4
4
3
Find the equation a line that is perpendicular to the line y = 3x - 1 and passes through the point (0, 3).
Perpendicular Lines
Lines that are perpendicular have gradients that are the negative reciprocal of each other; i.e. if one line
has a gradient of then the perpendicular line will have a gradient of - .
3
4
4
3
Find the equation a line that is perpendicular to the line y = 3x - 1 and passes through the point (0, 3).
Gradient is - and if it must pass through the point (0,3) then the equation is y = - x + 3.
1
3
1
3
Main Activity
Complete the Perpendicular lines sheet.
Main Activity 2
Complete the Perpendicular lines sheet.
y = -2x - 4.5
Key
Examples

Activities
Activity
Answers

Worked
Example

Worked
Example

Starter
What is the gradient of the green diagonal line?

What is the gradient of the red diagonal line?

What transformation takes the green triangle onto the red triangle?
Starter
What is the gradient of the green diagonal line?
2/3
What is the gradient of the red diagonal line?
-3/2
What transformation takes the green triangle onto the red triangle?
Rotation 90
anti-clockwise, centre (3,2)
o
Examples
A line is perpendicular to the line y + 2x - 4 = 0 and passes through the point (2, 3). Find the equation of the line.



A line is perpendicular to the line connecting the points (3,3) and (5,0) and passes through the point (3,3). Work out the equation of the line.
Examples
A line is perpendicular to the line y +2x - 4 = 0 and passes through the point (2, 3). Find the equation of the line.
y = x + c. When x = 2, y = 3 so 3 = (2) + c, so 3 = 1 + c
so c = 2. This means the equation is y = x + 2.

A line is perpendicular to the line connecting the points (3,3) and (5,0) and passes through the point (3,3). Work out the equation of the line.
Gradient between (3,3) and (5,0) = -
Perpendicular gradient =
y = x + c. When x = 3, y = 3 so 3 = (3) + c, so 3 = 2 + c so c = 1. This means the equation is y = x + 1
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2
1
2
1
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3
2
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2
3
Worked
Example

Main Activity
Fill in the reasons on the perpendicular bisectors sheet
Main Activity
Fill in the reasons on the perpendicular bisectors sheet
Full transcript