11x1 t05 05 perpendicular distance (2010)

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