Question

/
find the perpendicular distance from the
point (2, 1) to the line 3x-
4y=15
کر​

Answer 1

Answer:

2.6 units

Step-by-step explanation:

Given,

S = (2 , 1) = (x_1 , y_1)

3x - 4y = 15

To Find :-

Perpendicular distance between the points.

Solution :-

3x - 4y = 15

→ 3x - 4y - 15 = 0

Comparing "3x - 4y - 15 = 0" with "ax + by + c = 0" :-

→ a = 3 , b = - 4 , c = - 15

x_1 = 2 , y_1 = 1

Distance Formula :-

$\bf d=\dfrac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}$

Let's do :-

$=\dfrac{|3(2)-4(1)-15|}{\sqrt{(3)^2+(4)^2}}$

$=\dfrac{|6-4-15|}{\sqrt{9+16}}$

$=\dfrac{|6-19|}{\sqrt{25}}$

$=\dfrac{|-13|}{5}$

$=\dfrac{13}{5}$

= 2.6 units.

Know More :-

Distance formula :-

$\bf d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$