Answer :
Answer:
The value of b is 6
Step-by-step explanation:
Given as :
The points of line AB is A = ( 2 , b) and B = ( 4 , 10 )
So , Slop of this line is ( m 1) = [tex]\frac{y2-y1}{x2-x1}[/tex]
Or, ( m 1) = [tex]\frac{10-b}{4-2}[/tex]
Or, ( m 1) = [tex]\frac{10-b}{2}[/tex]
Again, Another line is
x + 3y = 6
Or, 3y = - x + 6
Or y = [tex]\frac{-1}{3}[/tex] x + [tex]\frac{6}{3}[/tex]
SO, Slope of this line is ( m 2 ) = [tex]\frac{-1}{3}[/tex]
∵ Both lines are perpendicular to each other
Then , ( m 1) × ( m 2) = - 1
or, ( m 1 ) × [tex]\frac{-1}{3}[/tex] = - 1
So, ( m 1 ) = 3
Now, ∵ ( m 1) = [tex]\frac{10-b}{2}[/tex]
∴ 3 = [tex]\frac{10-b}{2}[/tex]
Or, 10 - b = 6
∴ b = 10 - 6 = 4
Hence The value of b is 6 Answer