Respuesta :
GIven:
The equation is given as 7x-y-5 = 0.
The objective is to find the distance between the line and the origin.
Explanation:
Consider the coordinate of the origin as,
[tex](x_1,y_1)=(0,0)[/tex]The general form of straight line is,
[tex]ax_1+by_1+c=0[/tex]By comparing the coefficients of given equation with the general equation,
[tex]\begin{gathered} a=7 \\ b=-1 \\ c=-5 \end{gathered}[/tex]To find the distance:
The formula to find the distance between a point and the equation of a line is,
[tex]d=\frac{\lvert ax_1+by_1+c\rvert}{\sqrt[]{a^2+b^2}}\text{ . . . . ..(1)}[/tex]Substitute the obtained values in equation (1).
[tex]\begin{gathered} d=\frac{\lvert7(0)-1(0)-5\rvert}{\sqrt[]{(7)^2+(-1)^2}} \\ =\frac{\lvert-5\rvert}{\sqrt[]{49+1}} \\ =\frac{5}{\sqrt[]{50}} \\ =\frac{5}{5\sqrt[]{2}} \\ =\frac{1}{\sqrt[]{2}} \end{gathered}[/tex]Hence, the distance between the line and the origin is (1/√2).
