2. Perpendicular Distance
Formula
The shortest distance from a point to a line is the perpendicular distance.
3. Perpendicular Distance
Formula
The shortest distance from a point to a line is the perpendicular distance.
x1 , y1
4. Perpendicular Distance
Formula
The shortest distance from a point to a line is the perpendicular distance.
x1 , y1
Ax + By + C = 0
5. Perpendicular Distance
Formula
The shortest distance from a point to a line is the perpendicular distance.
x1 , y1
d
Ax + By + C = 0
6. Perpendicular Distance
Formula
The 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
Formula
The 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
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
8. Perpendicular Distance
Formula
The 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
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
1, 4
9. Perpendicular Distance
Formula
The 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
e.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
Formula
The 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
e.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
Formula
The 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
e.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
Formula
The 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
e.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
Formula
The 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
e.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
Formula
The 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
e.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, they
are on different sides of the line.
16. If Ax1 By1 C has different signs for different points, they
are on different sides of the line.
Ax + By + C = 0
17. If Ax1 By1 C has different signs for different points, they
are 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, they
are 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, they
are 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*