Question

Which is the distance between the point with the coordinates (1, 2) and the line with the equation 2x-3y=-2?

Answer 1

Eq. of line is 2x-3y+2=0
distance of (1,2) from 2x-3y+2=0 is
\[d=\frac{ \left| 2*1-3*2+2 \right| }{\sqrt{2^{2}+\left( -3 \right)^{2}}} \]
\[d=\frac{ 2 }{ \sqrt{13} }\]
this is the shortest distance.

Answer 2

can you give me the formula to this problem? thanks for showing me how to do it

Answer 3

If (x1,y1 ) be the point then distance (perpendicular) d from the line ax+by+c=0 is
\[d=\frac{ \left| ax1+by1+c \right| }{\sqrt{a ^{2}+b ^{2}} }\]