11 X1 T05 05 Perpendicular Distance

1. Perpendicular Distance
Formula

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.
( )
1 1
,x y

4. Perpendicular Distance
Formula
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
( )
1 1
,x y

5. Perpendicular Distance
Formula
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y

6. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y

7. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y

8. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y
( )1,4

9. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y
( )1,4
3x – 4y – 12 = 0

10. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y
( )1,4
3x – 4y – 12 = 0
r

11. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y
( )1,4
3x – 4y – 12 = 0
r
() ()
( )
22
3 1 4 4 12
3 4
r
- -
=
+ -

12. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
25
25
=
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y
( )1,4
3x – 4y – 12 = 0
r
() ()
( )
22
3 1 4 4 12
3 4
r
- -
=
+ -

13. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
25
25
=
5 units=
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y
( )1,4
3x – 4y – 12 = 0
r
() ()
( )
22
3 1 4 4 12
3 4
r
- -
=
+ -

14. Perpendicular Distance
Formula
1 1
2 2
Ax By C
d
A B
+ +
=
+
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and
centre (1,4).
25
25
=
5 units=
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d
( )
1 1
,x y
( )1,4
3x – 4y – 12 = 0
r
() ()
( )
22
3 1 4 4 12
3 4
r
- -
=
+ -
( ) ( )
2 2
the circle is
1 4 25x y
\
- + - =

15. If has different signs for different points, they are
on different sides of the line.
( )
1 1
Ax By C+ +

16. If has different signs for different points, they are
on different sides of the line.
( )
1 1
Ax By C+ +
Ax + By + C = 0

17. If has different signs for different points, they are
on different sides of the line.
( )
1 1
Ax By C+ +
Ax + By + C = 0
Ax + By + C > 0

18. If has different signs for different points, they are
on different sides of the line.
( )
1 1
Ax By C+ +
Ax + By + C = 0
Ax + By + C > 0
Ax + By + C < 0

19. If has different signs for different points, they are
on different sides of the line.
( )
1 1
Ax By C+ +
Exercise 5E; 1b, 2cf, 5a, 6a, 7bd, 8b,
9abc, 10, 13, 14, 18*
Ax + By + C = 0
Ax + By + C > 0
Ax + By + C < 0