Question

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

Answer 1

`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`