The distance from the origin to the line x + 2y-5 = 0 is___ ．

The distance from the origin to the line x + 2y-5 = 0 is___ ．

Analysis: according to the distance formula from point to line, d = | - 5| - 12 + 22 = 5

Find a point on the line x + y = 0 so that its distance to the origin is equal to that of the line x + 2Y - 5 = 0

Set point P (x, y)
x+y=0
sqrt(x^2+y^2)=abs(x+2y-5)/sqrt(5)
x=(5+5sqrt(10))/9
x=(5-5sqrt(10))/9

Find a point P on the line x + 2Y = o so that the distance from the origin is equal to the distance from the line x + 2y-3 = o

Let P coordinate be (m, n)
M+2N=0
The distance from P to the straight line x + 2y-3 = 0 is: | m + 2n-3 | / root (1 + 2 * 2) = 3 / root 5
The distance from P to the origin is: root (m ^ 2 + n ^ 2)
So: root (m ^ 2 + n ^ 2) = 3 / root 5
M^2+N^2=9/5
4N^2+N^2=9/5
N^2=9/25
N=+/-3/5
M=-/+6/5
So the P coordinates are: (6 / 5. - 3 / 5) and (- 6 / 5,3 / 5)