Chapter 4 Polynomials Maximum and Minimum problem Find the c

Chapter 4 Polynomials: Maximum and Minimum problem

Find the coordinates of the point on line y=3x+1 closet to (4,0)

Solution

Solution: Equation of line y=3x+1 , point (4,0).

We have to find the equation of normal to the line which passes through (4,0).

The slope of the normal will be -1/3

The equation of the line with slope -1/3 and passes through (x₁, y₁) = (4, 0) is

      y - y₁ = m(x - x₁)

     y - 0 = (-1/3)(x - 4)

or       y = (-1/3)x + 4/3.

To find the intersection of the normal line and y = 3x + 1, equating the two equation, we get
3x + 1 = (-1/3)x + 4/3

or      9x + 3 = -x + 4

or       10x = 1
Thus          x = 1/10    and    y = 3(1/10) + 1 = 13/10.

Therefore the point on the line closest to the point (4, 0) is (1/10, 13/10).                       Ans.