Question

find length of perpendicular from point p (2,5) on the line 2x+3y-6=0​

Answer 1

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Answer 2

Answer:

The length of the perpendicular from point p (2,5) on the line 2x+3y-6=0 is $\sqrt{13}$

Step-by-step explanation:

Given Information :The given point is P( 2,5) and the line on which it lies is 2x + 3y - 6 = 0

To Calculate: The length of the perpendicular from point P (2,5) to the line 2x + 3y - 6 = 0

Solution:

The formula for the length(D) of the perpendicular from a point  $(x_{1} ,y_{1} )$ and passing through the line Ax +By +C = 0 is given by

$D = \frac{Ax_{12} +By_{1} +C}{\sqrt{A^{2} +B^{2} } }$

Now, putting the values in the above equation, we get,

$D = \frac{2*2 +3*5 -6}{\sqrt{2^{2} +3^{2} } }=\frac{4 +15-6}{\sqrt{13} } =\frac{13}{\sqrt{13} } =\sqrt{13}$

Hence, The length of the perpendicular from point p (2,5) on the line 2x+3y-6=0 is $\sqrt{13}$

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