Question

What is distance between line 12x+35y+5=0 and point (2,0).

Answer 1

Answer:

The distance between line 12x+35y+5=0 and point (2,0) is $\frac{29}{37}$ units.

Step-by-step explanation:

The distance between a line $Ax+By+C=0$ and a point $(x_0,y_0)$ is

$d=\frac{Ax_0+By_0+C}{\sqrt{A^2+B^2}}$

The distance between line 12x+35y+5=0 and point (2,0) is

$d=\frac{12(2)+35(0)+5}{\sqrt{(12)^2+(35)^2}}$

$d=\frac{24+0+5}{\sqrt{144+1225}}$

On further simplification we get

$d=\frac{24+0+5}{\sqrt{1369}}$

$d=\frac{29}{37}$

Therefore, the distance between line 12x+35y+5=0 and point (2,0) is $\frac{29}{37}$ units.

Answer 2

Answer:

29 / 37

Step-by-step explanation:

The distance between a point (p, q) and a line ax + by + c = 0 is:

d = | ap + bq + c | / √(a² + b²)

Here, a = 12, b = 35, c = 5, p = 2, and q = 0.

d = | (12)(2) + (35)(0) + 5 | / √(12² + 35²)

d = 29 / 37