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Distance From Apointtoa Line

The document outlines the formula for calculating the distance from a point to a line, specifically in the form Ax + By + C = 0. It provides examples and assignments for finding the perpendicular distance from given points to specified lines. The formula is applicable for both vertical and horizontal lines, with specific calculations demonstrated for various points and lines.

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Abegail Villanueva
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51 views8 pages

Distance From Apointtoa Line

The document outlines the formula for calculating the distance from a point to a line, specifically in the form Ax + By + C = 0. It provides examples and assignments for finding the perpendicular distance from given points to specified lines. The formula is applicable for both vertical and horizontal lines, with specific calculations demonstrated for various points and lines.

Uploaded by

Abegail Villanueva
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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DISTANCE FROM

A POINT TO A
LINE
Objectives
1. Recall that the distance from a point (x1,y1) to the
line 𝐴𝑥+𝐵𝑦+𝐶=0 is given by the formula
d = 𝐴x1+𝐵y1+𝐶
2 2
√𝐴 +𝐵
2. Use the formula to calculate the distance from a point to a line (the
line may be given in vector form)
The distance from point (x1,y1) to a line (Ax1 + By1 + C = 0),
where both a and b cannot be equal to zero. If line is vertical or
horizontal, then the distance is just the horizontal/vertical
distance.

So, the distance (or perpendicular distance) D, from point P (x1,y1)


to a line L: Ax + By + C = 0 is given by
d = 𝐴x1+𝐵y1+𝐶
2 2
√𝐴 +𝐵
Find the length of perpendicular drawn from point A (1,9)
to the line -5x + 12y + 13 = 0.
Find the distance from the point (3,-4) to line 6x -
8y = 5.
Find the distance from point (2,1) to a line y = 2x + 1
Determine the distance between the origin and the line r =
(1,4) + s (2,1).
ASSIGNMENT:
Find the distance from the point with the given coordinates and
to the line with the given equation.
1. (-1, 5), 3x - 4y -1 = 0
2. (2,5), 5x – 12y = 1
3. 2x + 3y = 6; (7, 6)

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