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

Find the distance between the point p(0, 0) and

ashleypaz15

14.01.2022

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.

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