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2. Finding the Distance Between a point
and a Line
To find the perpendicular distance (which is also the
shortest distance) between a point and a line.
Where the point is P(x1, y1)
and the equation of the line in standard form is
Ax + By + C = 0
Ax1 + By1 + C
The distance is d = A2 + B2
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3. Example
Find the shortest distance between the point
P(1, 2)
and the line 5x + y ­ 1 = 0
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4. Example
Find the shortest distance between (3, 4) and the line
2x ­ 5y = 7
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5. For the lines x + 3y = 6 and x + 3y = 3
Find the
a) Horizontal distance between the lines
b) Vertical distance between the lines
c) Shortest distance between the lines
First, what is the slope of each of the lines and what does
this tell us about the lines?
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