What is the distance between the point of intersection of 6x+6y+8 = 0 and 6x+y=0 and the point (4,5).

The point of intersection of the lines 6x+6y+8 = 0 and
6x+y = 0 is got by solving the two equations.

(6x+6y+8)
-(6x+y) = 0

5y +8 = o

5y =
-8

y = -8/5. Substituting y = -8/5 in 6x+y = 0, we get 6x
-8/5 = 0. So x= (8/5)/6 = 8/30 =4/15

So the point P of
interesection = P (8/30.-8/5)

 Now to find the disyance
between (8/30 , -8/6) and (4,5) is

sqrt{ (4-4/15)^2 + (5-
(-8/5))^2}

= sqrt{ 56/15)^2
+(33/5)^2}

= 7.58
nealy.

Therefore the distance between the point of
intersection of the lines 6x+6y+8 = 0 and 6x+y = 0 and the point (4,5) is 7.58
nearly.