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

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) (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:

since the perpendicular line contains (0,0), the origin, you can substitute its x and y coordinates to the equation:

so, the equation of the perpendicular line is:

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:
eq1
eq2
Substitue x for y in eq2:

since y = x:

The point closest to the origin contained in line y = -x + 4 is (2,2).
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