Using the distance formula to find a point

Question

Find the point on the line –3x+3y–2=0 which is closest to the point (–5,0)

Answer 1

First solve for y......y=x+2/3.....so the typical point on this line has the coordinates (x,x+2/3). 

 

Now use that with the distance formula to the point that was given.

 

D=Sqrt( (x+5)² + (x+2/3)²)

 

D' = [2(x+5)+ 2(x+2/3)] / 2sqrt[(x+5)²+(x+2/3)²]

 

That equals zero when the numerator is 0 so

2x+10 + 2x +4/3 = 0

4x = -34/3

x = -34/12 = -17/6

 

Substitute in to find y the coordinate is (-17/6, -17/6+2/3) = (-17/6, -13/6)

 

Hope this helped