Question
The equation of a line is 2x - 3y = 12. Find the
perpendicular distance of the point (4, 5) from this line.Solution
The formula for the perpendicular distance of a point (x1, y1) from a line Ax + By + C = 0 is: Distance = |Ax1 + By1 + C| / β(AΒ² + BΒ²). For the line 2x - 3y = 12, rewrite it as 2x - 3y - 12 = 0. Substitute x1 = 4 and y1 = 5: Distance = |2(4) - 3(5) - 12| / β(2Β² + (-3)Β²) = |8 - 15 - 12| / β(4 + 9) = |-19| / β13 = 19 / β13 β 5.27 units.
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