**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 - .

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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.

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3

1

3

Main Activity

Complete the Perpendicular lines sheet.

Main Activity 2

Complete the Perpendicular lines sheet.

y = -2x - 4.5

**Key**

Examples

Examples

**Activities**

**Activity**

Answers

Answers

**Worked**

Example

Example

**Worked**

Example

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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**Worked**

Example

Example

Main Activity

Fill in the reasons on the perpendicular bisectors sheet

Main Activity

Fill in the reasons on the perpendicular bisectors sheet