Perpendicular Lines

Perpendicular Lines

Perpendicular lines meet at right angles

If you multiply gradients of

perpendicular lines you will

always get -1

Finding a Perpendicular Gradient

Find the numbers which are needed to make -1

-9

-5

-1/5

-2/7

-1/3

-1/7

1/9

1/5

7/2

-1

-1

-1

-1

-1

-1

Think about

the Do it

Now

How do

reciprocals

work?

y=3x-8

Gradient 1 x Gradient 2 = -1 for perpendicular lines

3 times -1/3

gives -1

So any line with a gradient

of -1/3 will be

perpendicular to y=3x-8

y=-1/3x+6

y=-1/3x+7

y=-1/3x-11

Calculate the gradient of a line perpendicular to the

following lines

1)  y=  2x-4

2)  y=  0.5x +6

3)  y=  x -5

4)  y=  4x -8

5)  y=  1/4x +2

6)  y=  0.25x -5

7)  y=  5x +6

8)  y=  8x -6

5 minutes

End

Hint: 1 divided by the number gives the

reciprocal- remember a perpendicular  line

will have the opposite gradient

Calculating more complicated

perpendicular gradients

How can we calculate a gradient

for a line perpendicular to y=3/5

x+4?

What is 1 divided by 3/5?

Hint: 1 divided by the number gives the

reciprocal- remember a perpendicular  line

will have the opposite gradient

Use the reciprocal button to find the

following reciprocals

1)  4/9

2)  1.25

3)  1/3

4)  2/7

5)  5

6)  5.75

7)  1.75

8)  6/7

4 minutes

End

Find the equation of the line which is perpendicular y=2x + 8 at the point

(1,10)

Gradient will be -0.5

Equation so far is y=-0.5x + c

We know it passes through (1,10) so put these values in

10=-0.5+ c

c must be 10.5

y=-0.5x + 10.5

Find the equation of the line which is perpendicular y=5x + 8 at the point

(5,33)

Gradient will be -1/5

Equation so far is y=-1/5x + c

We know it passes through (5,33) so put these values in

33=-1+ c

c must be 34

y=-2x + 34

Plenary

Find the equation of the line which is perpendicular to

y = 2x + 3

and passes through the point

(3, 9).

y = ½x + c

9 = ½(3) + c

3 = 1½ + c

4½ = c

y = ½x + 4½

-1 ÷ 2 = ½

Spot the mistakes:

Fluency

Fluency

L.O To be able to simplifying a ratio

Keywords

TIME

Gradient, Intercept, Straight Line, Co-ordinates, Plot,

Substitution, Parallel, Perpendicular, Reflection

L/Q:





Fluency

Fluency

Reasoning

Reasoning

Problem Solving

Problem Solving

Fluency

Fluency

Reasoning

Reasoning

Problem Solving

Problem Solving

Fluency

Fluency

Reasoning

Reasoning

Problem

Problem

Solving

Solving

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This content covers the concept of perpendicular lines in geometry and how to calculate gradients for lines perpendicular to given equations. Discover the relationship between perpendicular lines, their gradients, reciprocals, and the calculations involved in finding equations for such lines. Learn about finding perpendicular gradients and solving for equations at specific points.

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Presentation Transcript

27/02/2025 Perpendicular Lines

27/02/2025 Perpendicular Lines Perpendicular lines meet at right angles If you multiply gradients of perpendicular lines you will always get -1

27/02/2025 Finding a Perpendicular Gradient Find the numbers which are needed to make -1 3 x = -1 -1/3 Think about the Do it Now How do reciprocals work? 7 x = -1 -1/7 -9 x 1/9 = -1 -5 x 1/5 = -1 x 5 = -1 -1/5 x 7/2 = -1 -2/7

27/02/2025 Gradient 1 x Gradient 2 = -1 for perpendicular lines y=-1/3x+6 y=3x-8 y=-1/3x+7 y=-1/3x-11 3 times -1/3 gives -1 So any line with a gradient of -1/3 will be perpendicular to y=3x-8

27/02/2025 Calculate the gradient of a line perpendicular to the following lines 1) y= 2x-4 5 minutes 2) y= 0.5x +6 3) y= x -5 4) y= 4x -8 5) y= 1/4x +2 6) y= 0.25x -5 7) y= 5x +6 End 8) y= 8x -6 Hint: 1 divided by the number gives the reciprocal- remember a perpendicular line will have the opposite gradient

27/02/2025 Calculating more complicated perpendicular gradients How can we calculate a gradient for a line perpendicular to y=3/5 x+4? What is 1 divided by 3/5? Hint: 1 divided by the number gives the reciprocal- remember a perpendicular line will have the opposite gradient

27/02/2025 Use the reciprocal button to find the following reciprocals 1) 4/9 2) 1.25 3) 1/3 4) 2/7 5) 5 6) 5.75 7) 1.75 4 minutes End 8) 6/7

27/02/2025 Finding the equation of a line Finding the equation of a line Find the equation of the line which is perpendicular y=2x + 8 at the point (1,10) Gradient will be -0.5 Equation so far is y=-0.5x + c We know it passes through (1,10) so put these values in 10=-0.5+ c c must be 10.5 y=-0.5x + 10.5

27/02/2025 Example 2 Example 2 Find the equation of the line which is perpendicular y=5x + 8 at the point (5,33) Gradient will be -1/5 Equation so far is y=-1/5x + c We know it passes through (5,33) so put these values in 33=-1+ c c must be 34 y=-2x + 34

27/02/2025

27/02/2025 Plenary Spot the mistakes: Find the equation of the line which is perpendicular to y = 2x + 3 and passes through the point (3, 9). y = x + c 9 = (3) + c 3 = 1 + c 4 = c y = x + 4 -1 2 =

27/02/2025 I can work out intervals on a number line Fluency

27/02/2025 L/Q: TIME Power OF 3 5 Minute Timer 5 Minute Timer Gradient, Intercept, Straight Line, Co-ordinates, Plot, Substitution, Parallel, Perpendicular, Reflection Keywords