Question

length of perpendicular from origin to line 4x+3y-2=0is.....unit

Answer 1

The answer is given below :

FORMULA :

Let us consider any line be

ax + by + c = 0 .....(i)

Let, any point be (x1, y1).

Then, the required distance of the line (i) from the point (x1, y1) is given by

$= \frac{ |ax1 + by1 + c |}{ \sqrt{ {a}^{2} + {b}^{2} } } \: \: units$

So, the required distance from the origin O (0,0,0) is

$= \frac{ |c| }{ \sqrt{ {a}^{2} + {b}^{2} } } \: \: units$

SOLUTION :

The given line is

4x + 3y - 2 = 0 .....(ii)

Thus, the required distance of the line (ii) from the origin O (0,0,0) is

$= \frac{ | - 2| }{ \sqrt{ {4}^{2} + {3}^{2} } } \\ \\ = \frac{2}{ \sqrt{16 + 9} } \\ \\ = \frac{2}{ \sqrt{25} } \\ \\ = \frac{2}{ \sqrt{ {5}^{2} } } \\ \\ = \frac{2}{5} \: \: units$

which is the required length of the perpendicular line.

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