Answer:
The distance between the lines: 4x+3y-11 and 8x+6y=15 is [tex]\frac{7}{10}[/tex]
Step-by-step explanation:
You have two parallel and different lines. The form of the implicit equations is:
A*x + B*y + C= 0
A'*x + B'*y + C'=0
Since the two lines are parallel, the coefficients of their general equations must satisfy that the slopes are equal.
Therefore, the equations can be transformed so that the coefficients A and B are equal, multiplying or dividing one of them by a constant.
So, the distance between two lines can be expressed as follows:
[tex]d=\frac{|C-C'|}{\sqrt{A^{2} +B^{2} } }[/tex]
In this case, you have:
Then, you have:
Replacing in the definition of distance:
[tex]d=\frac{|-22-(-15)|}{\sqrt{8^{2} +6^{2} } }[/tex]
Solving:
[tex]d=\frac{|-7|}{\sqrt{8^{2} +6^{2} } }[/tex]
[tex]d=\frac{7}{\sqrt{8^{2} +6^{2} } }[/tex]
[tex]d=\frac{7}{\sqrt{64+36 } }[/tex]
[tex]d=\frac{7}{\sqrt{100 } }[/tex]
[tex]d=\frac{7}{10}[/tex]
The distance between the lines: 4x+3y-11 and 8x+6y=15 is [tex]\frac{7}{10}[/tex]