In this page perpendicular distance from a point to a straight line we
are going to see how to find the length of the perpendicular from a
given point.

The length of the perpendicular from the point (x₁,y₁) to the line ax + by + c = 0 is

| (ax₁ + by₁ + c)/ va² + b² |

**Example 1:**

Find the length of the perpendicular from (2,-3) to the straight line 2x - y + 9 = 0

**Solution :**

The length of the perpendicular from the point (x₁,y₁) to the line ax + by + c = 0 is

| (ax₁ + by₁ + c)/ va² + b² |

Here x₁ = 2 and y₁ = -3

= |(2(2) - (-3) + 9)/v(2² + (-1)²)|

= | (4 + 3 + 9)/v(4+1) |

= | 16/v5|

= 16/v5 units

**Example 2 :**

Find the length of the perpendicular from (5,2) to the straight line 3x+2y-1 = 0**Solution :**

The length of the perpendicular from the point (x₁,y₁) to the line ax + by + c = 0 is

| (ax₁ + by₁ + c)/ va² + b² |

Here x₁ = 5 and y₁ = 2

= |(3(5) + 2(2) - 1)/v(3² + (2)²)|

= | (15 + 4 - 1)/v(9+4) |

= | 18/v13|

= 18/v13 units

**Example 3 :**

Find the length of the perpendicular from (0,1) to the straight line x-3y+2 = 0**Solution :**

The length of the perpendicular from the point (x₁,y₁) to the line ax + by + c = 0 is

| (ax₁ + by₁ + c)/ va² + b² |

Here x₁ = 0 and y₁ = 1

= |(1(0) - 3(1) + 2)/v(1² + (-3)²)|

= | (0 - 3 + 2)/v(1+9) |

= | -1/v10|

= 1/v10 units

Related Topics

- Section formula
- Area of triangle
- Area of triangle worksheets
- Area of quadrilateral
- Centroid
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- Finding missing vertex using centroid worksheet
- Midpoint
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- Distance between two points worksheet
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- Equation of the line
- Equation of line using two points worksheet
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- Point of intersection of two lines
- Point of intersection Worksheets
- concurrency of straight line
- Concurrency of straight lines worksheet
- Circumcentre of a triangle
- Circumcentre of Triangle Worksheet
- Orthocentre of a triangle
- Orthocentre of Triangle Worksheet
- Incentre of a triangle
- Locus
- Angle between two straight lines
- Equation of a circle
- With center and radius
- With endpoints of a diameter
- Equation of a circle passing though three points
- Length of the tangent to a circle
- Equation of the tangent to a circle
- Family of circles
- Orthogonal circles
- Parabola
- Ellipse

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