Question

Find the distance between the two lines 3x-1 and x+3

Answer 1

The distance between lines is 0 units

Step-by-step explanation: the distance between both the lines is 0 as both the lines are intersecting at a single point (2,5).

Answer 2

Answer:  The distance between the given lines is 3.33.

Step-by-step explanation: The given lines are as follows:

$3x-1=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+3=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We have, from equations (i) and (ii) that

$3x-1=0\\\\\Rightarrow x=\dfrac{1}{3}$

and

$x+3=0\\\\\Rightarrow x=-3.$

Therefore, the distance between the two points

$=\big|-3-\dfrac{1}{3}\big|\\=\big|-\dfrac{10}{3}\big|\\\\=\dfrac{10}{3}.$

Thus, the distance between the given lines is 3.33.