Question

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

Answer 1

Answer:

The distance between the point P(0, 0) and the line y = −x + 4 is $2\sqrt{2}$ units.

Step-by-step explanation:

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

$d=\dfrac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}}$

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

$d=\dfrac{|0+0-4|}{\sqrt{1^2+1^2}}$

$d=\dfrac{|-4|}{\sqrt{2}}$

$d=\dfrac{4}{\sqrt{2}}$

Rationalize denominator.

$d=\dfrac{4}{\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}$

$d=\dfrac{4\sqrt{2}}{2}$

$d=2\sqrt{2}$

Therefore, the distance between the point P(0, 0) and the line y = −x + 4 is $2\sqrt{2}$ units.