Question

find the distance between two parallel line whes the equations are 3x-5y+7=0 and 6x-10y-5=0​

Answer 1

Answer:

1st equation : 3x - 5y + 7 = 0

2nd equation : 6x - 10y - 5 = 0

2nd equation : 2 ( 3x - 5y) = 5

2nd equation : 3x - 5y - 5/2 = 0

Using Distance formula b/w parallel lines,

Here, A = 3, B = -5, C1 = 7, C2 = -5/2

d = $\mathsf{\dfrac{|C_1\:-C_2|}{\sqrt{{A}^{2}\:+\:{B}^{2}}}}$

d = $\mathsf{\dfrac{|7\:-\:(-5/2)|}{\sqrt{{3}^{2}\:+\:{(-5)}^{2}}}}$

d = $\mathsf{\dfrac{|7\:+\:5/2)|}{\sqrt{9\:+\:25}}}$

d = $\mathsf{\dfrac{|19/2)|}{\sqrt{34}}}$

❇️ d = $\mathsf{\dfrac{19}{2{\sqrt{34}}}}$ ❇️

↪️ Hence, Distance between them is $\mathsf{\dfrac{19}{2{\sqrt{34}}}}$ units.