Question

Find the distance of the points A(3,6)B(-7,8) from the line 4x+6y-8=0?

Answer 1

`20/sqrt13, and, 6/sqrt13," resp."`

Explanation:

Recall that the distance of a point `P(x_1,y_1)` from the line

`L : ax+by+c=0` is denoted by, `d(P,L),` and is given by,

`d=(|ax_1+by_1+c|)/sqrt(a^2+v^2).`

`:. d(A,L)=(|4(3)+6(6)-8|)/sqrt(4^2+6^2)=40/sqrt52=20/sqrt13, and,`

`d(B,L)={|4(-7)+6(8)-8|)/sqrt(4^2+6^2)=12/sqrt52=6/sqrt13.`