Find the point on the line y = 3x + 2 that is closest to the origin.

The point on the line that is closest to the origin is .

Given,  , whose slope is .

Let is the slope of the line perpendicular to the above line.

So,

Then, the general equation of a line perpendicular line will be .

So the equation line passing through the origin and perpendicular to the line is , .

Then the closest point will be the intersection point of these two lines, i.e.

and

Therefore, the point on the line that is closest to the origin is .

Know more about the slope of a straight line here:

link

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)