Question

find the distance between the lines 3x-4y+9=0and6x-8y-17=0

Answer 1

➡HERE IS YOUR ANSWER⬇

♧♧FORMULA♧♧

We consider two parallel lines :

ax + by = p

and

ax + by = q

The distance between these parallel lines is given by

$= \frac{ |p - q| }{ \sqrt{ {a}^{2} + {b}^{2} } } \: \: units$

♧♧SOLUTION♧♧

The parallel lines are :

3x - 4y = -9 .....(i)

and

6x - 8y = 17

=> 3x - 4y = 17/2 .....(ii)

Applying formula, we get the required distance

$= \frac{ | - 9 - \frac{17}{2} | }{ \sqrt{ {3}^{2} + {( - 4)}^{2} } } \: units \\ \\ = \frac{ \frac{35}{2} }{ \sqrt{9 + 16} } \: units \\ \\ = \frac{ \frac{35}{2} }{ \sqrt{25} } \: units \\ \\ = \frac{35}{2 \times 5} \: units \\ \\ = \frac{7}{2} \: units \\ \\ = 3.5 \: units$

⬆HOPE THIS HELPS YOU⬅