11 x1 t05 05 perpendicular distance (2013)
TRANSCRIPT
Perpendicular Distance Formula
Perpendicular Distance Formula
The shortest distance from a point to a line is the perpendicular distance.
Perpendicular Distance Formula
The shortest distance from a point to a line is the perpendicular distance. 1 1,x y
Perpendicular Distance Formula
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
1 1,x y
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
Perpendicular Distance Formula
1 12 2
Ax By Cd
A B
The shortest distance from a point to a line is the perpendicular distance.
Ax + By + C = 0
d 1 1,x y
Perpendicular Distance Formula
1 12 2
Ax By Cd
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
Perpendicular Distance Formula
1 12 2
Ax By Cd
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
Perpendicular Distance Formula
1 12 2
Ax By Cd
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
Perpendicular Distance Formula
1 12 2
Ax By Cd
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
Perpendicular Distance Formula
1 12 2
Ax By Cd
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 4r
Perpendicular Distance Formula
1 12 2
Ax By Cd
A B
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4).
2525
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 4r
Perpendicular Distance Formula
1 12 2
Ax By Cd
A B
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4).
2525
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 4r
Perpendicular Distance Formula
1 12 2
Ax By Cd
A B
e.g. Find the equation of the circle with tangent 3x – 4y – 12 = 0 and centre (1,4).
2525
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 4r
2 2
the circle is
1 4 25x y
If has different signs for different points, they are on different sides of the line.
1 1Ax By C
If has different signs for different points, they are on different sides of the line.
1 1Ax By C
Ax + By + C = 0
If has different signs for different points, they are on different sides of the line.
1 1Ax By C
Ax + By + C = 0
Ax + By + C > 0
If has different signs for different points, they are on different sides of the line.
1 1Ax By C
Ax + By + C = 0
Ax + By + C > 0Ax + By + C < 0
If has different signs for different points, they are on different sides of the line.
1 1Ax By C
Exercise 5E; 1b, 2cf, 5a, 6a, 7bd, 8b, 9abc, 10, 13, 14, 18*
Ax + By + C = 0
Ax + By + C > 0Ax + By + C < 0