IGCSE Chapter 15 Parpendicular Lines .pptx

Check line are perpendicular or not

1. Chapter 15.7 Perpendicular Lines

2. Thursday, 03 November 2022 Starter Write down the equation of a line parallel to… y = 8 x + 6 y = 8x – 29 y = 8x y = 8x – ¼ y = 8x - 10 y = 8x + 1 y = 8x + 5 y = 8x + 2 y = 8x – 6

3. What do you know about perpendicular lines? To prove two lines are perpendicular, the product of their gradients will be -1. They meet at a right-angle. They meet at a right-angle. Real-life examples the point where two city roads intersect floor tiles

4. Perpendicular Lines Gradients : Opposite sign, reciprocal Two lines are perpendicular, the product of their gradients will be -1.

5. Identify perpendicular lines Find the equation of perpendicular line that passes through a point. Objectives

6. Thursday, 03 November 2022 Introduction : Perpendicular Lines. Investigation (Part 2): The graph drawn has a gradient of 2. What is the equation of that line? y = 2x – 1 Draw the graph of y = -½x – 1. What do you notice about the lines…? They are perpendicular They meet at right angles!

7. Thursday, 03 November 2022 Parallel and Perpendicular Lines. Investigation (Part 2): We’ve established that these pairs of lines are perpendicular. What similarity do you notice between these pairs of lines…? y = 2x – 1 y = -½x – 1 y = -¼x + 2 y = 4x – 2 Think about the gradients of each pair of lines. Multiply them together. What do you get? 2 x -½ = -1 -¼ x 4 = -1 The gradients of two perpendicular lines multiply to make -1.

8. Perpendicular Lines …Perpendicular lines gradients are negative reciprocal of each other…!

9. Line 1: Line 2: If line L1 and L2 are perpendicular to each other then     Perpendicular Lines.

10. Thursday, 03 November 2022 Parallel and Perpendicular Lines. Fill in the Gaps: Fill in the gaps in the following calculations (use the rules that we learnt on the last few slides). 3 x -1/3___ = -1 7 x -1/7____ = -1 -9 x 1/9 = -1 4) -5 x 1/5 = -1 5) x _5__ = -1 6) x _-7/2____ = -1              

11. Thursday, 03 November 2022 Lesson Objective: To be able to find the equation of graphs parallel or perpendicular to others and passing through a specific point. Parallel and Perpendicular Lines. Keywords: Equation  y = mx + c  Negative Reciprocal  Parallel  Perpendicular. The ‘Negative Reciprocal’: In fact, the gradient of a line perpendicular to another is the negative reciprocal of the original line. The reciprocal of a number is defined as 1 divided by the number. If a line has a gradient of -2, the perpendicular line has a gradient of: -   =  

12. Example. Perpendicular Lines A)   Y= -1/2x +7 Y= 4x+6

13. Activity 1

14. Thursday, 03 November 2022 Activity 1: Perpendicular Lines.

15. Thursday, 03 November 2022 Objective 2: Find the equation of line perpendicular to others and passing through a specific point. Find the equation of the line perpendicular to y = - x – 2 and passing through the point (2, 9).   What is the gradient of the line given…? y = - x – 2   = -   y = 3x + c   To find the value of c, substitute your pair of coordinates into the equation… sub ( 2 , 9 )  y = 3x + c 9 = 3( 2 ) + c 9 = 6 + c 3 = c So, the equation is … y = 3x + 3. …remember the negative reciprocal…!

16. Thursday, 03 November 2022 Perpendicular Lines. Equations of Perpendicular Lines: Find the equation of the line perpendicular to y = 2x + 4 and passing through the point (3, 7). What is the gradient of the line given…? y = 2x + 4 = 2 y = x + c   To find the value of c, substitute your pair of coordinates into the equation… sub ( 3 , 7 )  7 = ( 3 ) + c   7 = + c   = c   So, the equation is … y = x + .   …remember the negative reciprocal …! = c  

17. Thursday, 03 November 2022 Activity 2: Perpendicular Lines. Find the equation of the line which is perpendicular to y = x + 1 and passes through (5, 21). Find the equation of the line which is perpendicular to 10y + 5x = 3 and passes through (-7, -1). Find the equation of the line which is perpendicular to 2x = 8 – y and passes through (16, 47). Find the equation of the line which is perpendicular to 6 + 8y = 3x and passes through (12, -37).  

18. Thursday, 03 November 2022 Perpendicular Lines. End of Lesson Reflection: . How do you feel about finding the equations of perpendicular lines now?

19. Thursday, 03 November 2022 Plenary: Perpendicular Lines. Exit Ticket: What is the relationship shared by parallel lines? What is the relationship between two perpendicular lines?

20. H.W And TND H.W. Q.3, Q.4 and Q.5 - 2 sub questions from each.