Question

Use MuPAD to find the point on the line y = 2 – x/3 that is closest to the point x = -3, y = 1.

 

 

Answer 1

The distance between two points (x1, y1) and (x2, y2) is given by the formula

d = √{(x1, x2)2 + (y1, y2)2}

 

A co-ordinate on the line can be obtained in terms of y. That point can be used to find the distance between the point on the line and (-3, 1). Finally, the function obtained can be differentiated and solved to find the root and minimum distance.

 

Now, our line is:

y = 2 – x/3

3y + x – 6 = 0

 

Therefore, point on the line is (6 – 3y, y).

 

The distance is

d = √{(6 – 3y + 3)2 + (y – 1)2}

 

We need to minimize the above function in MATLAB

 

The MATLAB code is given below:

 

Input:

syms y

d = (6-3*y+3)^2 + (y-1)^2;

dif = diff(d)

solve(dif)

 

Output:

 

Therefore,

y = 14/5

x = 6 – 3y

x = 6 – 42/5 = -2.4

Therefore,

y = 14/5

x = 6 – 3y

x = 6 – 42/5 = -2.4