Perpendicular Length is defined as the length of the perpendicular from point (x1, y1) to the line Ax+By+C=0

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Formula

Perpendicular Length/ Distance

(+ - )Ax1+By1+C /√A^{2}+B^{2}

(+ - )Ax1+By1+C /√A

Find the length of the perpendicular from the point (2,3) on the line x + 2y + 5 = 0.

x1 = 2, y1 = 3,

A = 1, B = 2, C = 5

**Apply Formula:**

(+ - )Ax1+By1+C /√A^{2}+B^{2}

(1*2)+ (2*3)+5/√1^{2}+2^{2}

=2+6 +5 /√1+4

=13/√5

=13/2.23

=**5.28 or 6**