SOLUTION: Write the equation of the line passing through the two points. show that this line is perpendicular to the given line. (4,2) and (-4,6); y=2x+3

Algebra ->  Systems-of-equations -> SOLUTION: Write the equation of the line passing through the two points. show that this line is perpendicular to the given line. (4,2) and (-4,6); y=2x+3      Log On


   

Question 123320: Write the equation of the line passing through the two points. show that this line is perpendicular to the given line.
(4,2) and (-4,6); y=2x+3
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
Equation of the point passing through 2 points is given by:

%28y+-+y1%29%2F%28y2+-+y1%29 = %28x+-+x1%29%2F%28x2+-+x1%29+

The two points are: (4, 2) and (-4, 6)

plugging in these points:

%28y+-+2%29%2F%286+-+2%29 = %28x+-+4%29%2F%28-4+-+4%29

%28y+-+2%29%2F4+ = %28x+-+4%29%2F%28-8%29

==> (y - 2) = %28x+-+4%29%28-1%2F2%29

This can be written as:

==> 2(y - 2) = (-)(x - 4)

==> 2y - 4 = -x + 4

==> 2y + x - 4 - 4 = 0

==> 2y + x - 8 = 0

Or ==> y = -x/2 + 4 -------------------(1)

This is the equation of the line.

So now to check whether the above equation is perpendicular to the given line
y = 2x + 3 --------------------------(2)

For thsi condition to satisfy the product of their slopes should be equal to negative 1.

So first lets find the slope of eqn (1) ==> m1 = -1/2

Slope of eqn (2) ==> m2 = 2

So now the product of m1 & m2 = (-1/2) * (2) = -1

Hence both the lines are penpendicular.

Regards