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- 1. Perpendicular Distance Formula
- 2. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance.
- 3. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1
- 4. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 Ax + By + C = 0
- 5. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax + By + C = 0
- 6. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0
- 7. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4).
- 8. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4). 1, 4
- 9. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4). 3x – 4y – 12 = 0 1, 4
- 10. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4). 3x – 4y – 12 = 0 r 1, 4
- 11. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4). 3 1 4 4 12 r 3x – 4y – 12 = 0 3 4 2 2 r 1, 4
- 12. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4). 3 1 4 4 12 r 3x – 4y – 12 = 0 3 4 2 2 r 25 1, 4 25
- 13. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4). 3 1 4 4 12 r 3x – 4y – 12 = 0 3 4 2 2 r 25 1, 4 25 5 units
- 14. Perpendicular Distance FormulaThe shortest distance from a point to a line is the perpendicular distance. x1 , y1 d Ax1 By1 C d A2 B 2 Ax + By + C = 0e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4). 3 1 4 4 12 r 3x – 4y – 12 = 0 3 4 2 2 r 25 the circle is 1, 4 25 x 1 y 4 25 2 2 5 units
- 15. If Ax1 By1 C has different signs for different points, theyare on different sides of the line.
- 16. If Ax1 By1 C has different signs for different points, theyare on different sides of the line. Ax + By + C = 0
- 17. If Ax1 By1 C has different signs for different points, theyare on different sides of the line. Ax + By + C > 0 Ax + By + C = 0
- 18. If Ax1 By1 C has different signs for different points, theyare on different sides of the line. Ax + By + C > 0 Ax + By + C < 0 Ax + By + C = 0
- 19. If Ax1 By1 C has different signs for different points, theyare on different sides of the line. Ax + By + C > 0 Ax + By + C < 0 Ax + By + C = 0 Exercise 5E; 1b, 2cf, 5a, 6a, 7bd, 8b, 9abc, 10, 13, 14, 18*

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