This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1918 Excerpt: ...Thus, for all points P on the opposite side of AB from the origin, d would be positive, and for all points P on the same side of AB as the origin, d would be negative. The student should now verify the fact that the formula (3) above gives the sign of d correctly according to this agreement. Every straight line thus ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1918 Excerpt: ...Thus, for all points P on the opposite side of AB from the origin, d would be positive, and for all points P on the same side of AB as the origin, d would be negative. The student should now verify the fact that the formula (3) above gives the sign of d correctly according to this agreement. Every straight line thus divides the plane into two parts, which may be called the positive and negative sides of the line. The origin is, then, always on the negative side of any line (unless the line passes through the origin, in which case the upper side of the bine is Draw the figure and note that the result thus obtained by the formula is correct in sign as well as numerically. 2. Find the distance from the line 3a; + 4y + l = 0 to each of the points (-1, -3), (2, 5), and (0, -4). 3. Find the distance from the line y--2 x = 0 to each of the points (3, -2), (1, 4), and (-2, 2). 4. Find the equation of the locus of a point that moves so as to be equally distant from the lines the positive side) (see Fig. 70). EXERCISES 1. How far is the point (1, 4) from the line a: + y + l = 0? Solution. Using the formula (4), . axx + byx + c Solution. Let P = (x, y) be any point on the locus, and and rf2 the distances from the given lines to the point P (Fig. 74). Since the point P is equally distant from the lines (1) and (2), we must have either, -i = -2 (A) contains all points equally distant from (1) and (2) for which the distances are both positive or both negative; (B) contains all points equally distant from (1) and (2) for which one of the distances is positive and the other negative. These loci are of course the bisectors of the angles formed by the lines (1) and (2), and (A) is the one passing through the angle containing the origin. The simplified forms of the equ
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