Question

(Problem in two-dimensions.) Given the line: L1 : y = 2x , (2) find the equation of the line L2 perpendicular to L1 passing through the point P = (1, 2).

Answer 1

Given :

Equation of line 1 , y = 2x .

A point (1 , 2) .

To Find :

The equation of the line L2 perpendicular to L1 passing through the point P = (1, 2) .

Solution :

Let , equation of line 2 is :

y = mx + c .....eq 1 ( here , m is slope and c is a constant )

Now , we know when two lines are perpendicular product of their slope is -1 .

Slope of given line is 2 .

Therefore ,

`2m=-1\\\\m=(-1)/(2)`

Now putting value of m in equation 1 , we get :

`y=(-1)/(2)x+c`

Now , it is given that this point (1,2) satisfy the above equation .

So ,

`2=(-1)/(2)(1)+c\\\\c=(5)/(2)`

Putting value of c in above equation , we get :

`y=-(1)/(2)x+(5)/(2)\\\\2y=-x+5`

Therefore , the equation of the line L2 perpendicular to L1 passing through the point P = (1, 2) is 2y = -x +5 .

Hence , this is the required solution.