Question

Find the distance between the point P(0, 0) and the line y = −x + 4 using the distance formula

Answer 1

The distance between the point P(0, 0) and the line y = −x + 4 is
`2√(2)` units.

Explanation:

Distance between the point
`(x_0,y_0)` and the line
`ax+by+c=0` is

`d=(|ax_0+by_0+c|)/(√(a^2+b^2))`

The given equation is

`y=-x+4`

Taking all terms on the left side.

`x+y-4=0`

The distance between the point
`(0,0)` and the line
`x+y-4=0` is

`d=(|0+0-4|)/(√(1^2+1^2))`

`d=(|-4|)/(√(2))`

`d=(4)/(√(2))`

Rationalize denominator.

`d=(4)/(√(2))* (√(2))/(√(2))`

`d=(4√(2))/(2)`

`d=2√(2)`

Therefore, the distance between the point P(0, 0) and the line y = −x + 4 is
`2√(2)` units.