10 Perpendicular Lines
0 likes1,115 views
The document explains the concept of perpendicular lines and their gradients, emphasizing that to find the gradient of a line perpendicular to a given line, one should flip the fraction and change the sign. It includes examples demonstrating how to calculate the gradients of specific lines and prove their perpendicularity using the product of their gradients being -1. The document also references exercises from Heinemann for practice.
1 of 8
More Related Content
What's hot (20)
Ad
Viewers also liked (14)
Ad
Similar to 10 Perpendicular Lines (20)
Recently uploaded (20)
10 Perpendicular Lines
- 2. A (4, 4) D (-4, 4) B (4, -4) C (-4, -4) 90 0 90 0
- 3. Perpendicular Lines 0 y x A (a , b) B (-b , a) After a 90 0 rotation (anti-clockwise) A moves to B As both lines go through origin gradients are: 90 0 NB Fraction has been turned upside down and turned into negative
- 4. Copy the following: For perpendicular lines: 1. Lines are perpendicular 2. To find gradient of line perpendicular to given line think: “ Flip the fraction and change the sign”
- 5. Example 1 What is the gradient of a line perpendicular to the line through the points P (4 , 7) and Q (5 , 11) ? Solution : Find gradient between given points Flip fraction- change sign 2. Use m 1 x m 2 = -1 to find gradient of perpendicular line.
- 6. Example 2 Two lines have equations 3x + 2y - 7 = 0 & 4x - 6y + 1 = 0 Prove that they are perpendicular. Solution : Find the gradient of line 1 by rearranging and using y = mx + c Line 1 3x + 2y - 7 = 0 2y = -3x + 7 Gradient 1 = -3/2 Line 2 4x - 6y + 1 = 0 6y = 4x + 1 Gradient 2 = 2/3 2. Find the gradient of line 2 by rearranging and using y = mx + c
- 7. Example 2 Two lines have equations 3x + 2y - 7 = 0 & 4x - 6y + 1 = 0 Prove that they are perpendicular. Solution : 3. Check that m 1 x m 2 = -1 4. Make statement Since m 1 x m 2 = -1 lines are perpendicular
- 8. Heinemann, p.6, Ex 1D, Q1, 2, 3 & 6