Page 215 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Let be any point on the line, and position the vector so that its initial point is at Q.
By virtue of Example 5, the vector n is perpendicular to the line (Figure 3.3.8). As indicated in the figure, the distance D is
equal to the length of the orthogonal projection of on n; thus, from 10,

But

so

Since the point lies on the line, its coordinates satisfy the equation of the line, so (12)
(13)
Substituting this expression in 12 yields the formula

Figure 3.3.8 is

EXAMPLE 8 Using the Distance Formula
It follows from Formula 13 that the distance D from the point (1, ) to the line

Exercise Set 3.3

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