SOLUTION: I need to find the coordinates (x,y) of the point on the graph of y=-x+4 that is closest to the origin.I already found the point that minimize the square but then I don't know what

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to find the coordinates (x,y) of the point on the graph of y=-x+4 that is closest to the origin.I already found the point that minimize the square but then I don't know what      Log On


   

Question 105945: I need to find the coordinates (x,y) of the point on the graph of y=-x+4 that is closest to the origin.I already found the point that minimize the square but then I don't know what to do.
Thanks for you help
eska
Answer by alvinjohnburgos(11) About Me  (Show Source):
You can put this solution on YOUR website!
In geometry, the shortest distance between a line and a point is a perpendicular segment connecting them. By definition of a perpendicular line:
slope of the perpendicular line = negative reciprocal of slope the line perpendicular to that line
So:
y+=+mx+%2B+b
y+=+-%281%2F-1%29x+%2B+b
y+=+x+%2B+b%29
since the perpendicular line contains (0,0), the origin, you can substitute its x and y coordinates to the equation:
y+=+-x+%2B+b
0+=+0+%2B+b
b+=+0
so, the equation of the perpendicular line is:
y+=+x
since the point closest to the origin in the line is the intersection of that line to the perpendicular line, we will solve for y and x:
eq1y+=+x
eq2y+=+-x+%2B+4
Substitue x for y in eq2:
y+=+-x+%2B+4
x+=+-x+%2B+4
2x+=+4
x+=+2
since y = x:
y+=+2
The point closest to the origin contained in line y = -x + 4 is (2,2).