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s4.4.5

Distance Between a Point and a Line

1,000 questions

To find the distance from a point (x0,y0)(x_0, y_0) to a line ax+by+c=0ax+by+c=0, use the formula:

Distance = ax0+by0+ca2+b2\frac{|ax_0 + by_0 + c|}{\sqrt{a^2 + b^2}}

This involves substituting the point's coordinates into the line's equation for the numerator, and dividing by the magnitude of the normal vector of the line. Typically, the coefficients aa and bb will form a Pythagorean triple to simplify the denominator.

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