What is the distance from the origin to the point on the line y=-2x+2 that is closest to the origin?

1 Answer

2/\sqrt5\ \text{unit

Explanation:

The distance, from origin (0, 0) to the point on the line: y=-2x+2 that is closest to the origin, will be equal to the length of perpendicular drawn from origin (x_1, y_1)\equiv(0, 0) to the line: y=-2x+2 or 2x+y-2=0

The minimum distance of given line from origin will be given by following formula

\frac{|ax_1+by_1+c|}{\sqrt{a^2+b^2}}

=\frac{|2(0)+0-2|}{\sqrt{2^2+1^2}}

=2/\sqrt5\ \text{unit