(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).

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 ,

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

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

So ,

Putting value of c in above equation , we get :

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.

Step-by-step explanation:

Integers are whole numbers which are positive or negative.

Rational expressions is fraction which has numerator or denominator.

Division of integers is the opposite operation of multiplying integers. It is like dividing whole numbers. You only have to take not of the positive or negative sign of each integer to determine the sign of the quotient.

Division of rational expression is different. It takes few steps to solve the rational expression.

1) Flip the second term of the expression and multiply.

2) factor out the numerator and denominator

3) cancel out the common factor/ duplicate factors and simplify