Question

length of perpendicular from (1, 1) to the line 5x +12y+9=0​

Answer 1

SOLUTION

TO DETERMINE

The length of the perpendicular from (1, 1) to the line 5x + 12y + 9 = 0

EVALUATION

Here the given point is (1,1)

Equation of the line is 5x + 12y + 9 = 0

Hence the required length of the perpendicular from (1, 1) to the line 5x + 12y + 9 = 0 is

$\displaystyle \sf{ = \bigg| \: \frac{(5 \times 1) + (12 \times 1) + 9}{ \sqrt{ {5}^{2} + {12}^{2} } } \: \bigg| } \: \: \: unit$

$\displaystyle \sf{ = \bigg| \: \frac{5 + 12+ 9}{ \sqrt{25 + 144 } } \: \bigg| } \: \: \: unit$

$\displaystyle \sf{ = \bigg| \: \frac{26}{ \sqrt{169 } } \: \bigg| } \: \: \: unit$

$\displaystyle \sf{ = \bigg| \: \frac{26}{13 } \: \bigg| } \: \: \: unit$

$\displaystyle \sf{ = 2 \: } \: \: \: unit$

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