11X1 T05 05 perpendicular distance (2010)

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  • 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 CdA 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 CdA 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 CdA 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 CdA 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

    1,43x 4y 12 = 0

  • Perpendicular Distance Formula

    1 12 2

    Ax By CdA 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

    1,43x 4y 12 = 0

    r

  • Perpendicular Distance Formula

    1 12 2

    Ax By CdA 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

    1,43x 4y 12 = 0

    r

    22

    3 1 4 4 12

    3 4r

  • Perpendicular Distance Formula

    1 12 2

    Ax By CdA 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

    1,43x 4y 12 = 0

    r

    22

    3 1 4 4 12

    3 4r

  • Perpendicular Distance Formula

    1 12 2

    Ax By CdA 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

    1,43x 4y 12 = 0

    r

    22

    3 1 4 4 12

    3 4r

  • Perpendicular Distance Formula

    1 12 2

    Ax By CdA 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

    1,43x 4y 12 = 0

    r

    22

    3 1 4 4 12

    3 4r

    2 2the 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

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