Question

find the length of the perpendicular distance from (-2 -3) to the straight line 5x-2y +4=0​

Answer 1

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FORMULA TO BE IMPLEMENTED :

If the equation of a line is

$ax + by + c = 0$

Then the Perpendicular Distance from the point $( x_1, y_1 )$

is given by

$\: = \displaystyle \: | \:\frac{(a x_1 + b y_1 + c ) }{ \sqrt{ {a}^{2} + {b}^{2} } } \: |$

CALCULATION :

The given equation of the line is

$5x - 2y + 4 = 0$

The given point is (-2 ,-3 )

So the length of the perpendicular distance from (-2 -3) to the straight line 5x-2y +4=0 is

$\: = \displaystyle \: | \:\frac{(5 \times ( - 2) + ( -3 ) \times ( - 2) + 4 ) }{ \sqrt{ {( - 5)}^{2} + {( - 2)}^{2} } } \: |$

= 0 unit

EXPLANATION FOR SUCH RESULT :

Since (-2 -3) is a point on the straight line 5x-2y +4=0

So the required distance = 0