(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.

d? maybe

step-by-step explanation:

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above