Question

Find the length of the perpendicular from the point (2, 3) to the line
3x + 4y = 5.​

Answer 1

Topic :-

Straight Line

Given :-

A perpendicular is drawn from the point (2, 3) to the line 3x + 4y = 5.

To Find :-

Length of the perpendicular drawn.

Concept Used :-

Length of perpendicular from a point (h, k) on the line ax + by + c = 0 is given by :-

$\sf {\left | \dfrac{ah+bk+c}{\sqrt{a^2+b^2}} \right |}$

Solution :-

It is given that, a perpendicular is drawn from the point (2, 3) to the line 3x + 4y = 5.

$\sf{(2,3)\equiv (h,k)}$

h = 2

k = 3

We can write equation of line as :-

3x + 4y - 5 = 0

On comparing it with ax + by + c = 0, we can say,

a = 3

b = 4

c = -5

Applying formula,

$\sf {Length\:of\:perpendicular=\left | \dfrac{ah+bk+c}{\sqrt{a^2+b^2}} \right |}$

Substituting values,

$\sf {Length\:of\:perpendicular=\left | \dfrac{3(2)+4(3)-5}{\sqrt{3^2+4^2}} \right |\:units}$

$\sf {Length\:of\:perpendicular=\left | \dfrac{6+12-5}{\sqrt{9+16}} \right |\:units}$

$\sf {Length\:of\:perpendicular=\left | \dfrac{13}{\sqrt{25}} \right |\:units}$

$\sf {Length\:of\:perpendicular=\dfrac{13}{5}\:units }$

$\sf {Length\:of\:perpendicular=2.60\:units }$

Answer :-

So, the length of perpendicular from the point (2, 3) to the line 3x + 4y = 5 is 2.60 units.