Mathematics: The points a(2,b) and b(4,10) lie on a line. the line x + 3y - 6=0 is perpendicular to this line. what is the value of b?

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The points a(2,b) and b(4,10) lie on a line. the

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08.01.2022

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) = $\frac{y2-y1}{x2-x1}$

Or, ( m 1) = $\frac{10-b}{4-2}$

Or, ( m 1) = $\frac{10-b}{2}$

Again, Another line is

x + 3y = 6

Or, 3y = - x + 6

Or y = $\frac{-1}{3}$ x + $\frac{6}{3}$

SO, Slope of this line is ( m 2 ) = $\frac{-1}{3}$

∵ Both lines are perpendicular to each other

Then , ( m 1) × ( m 2) = - 1

or, ( m 1 ) × $\frac{-1}{3}$ = - 1

So, ( m 1 ) = 3

Now, ∵ ( m 1) = $\frac{10-b}{2}$

∴ 3 = $\frac{10-b}{2}$

Or, 10 - b = 6

∴ b = 10 - 6 = 4

Hence The value of b is 6 Answer

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