Friday, December 25, 2009

`(-2, 8), y = -3x + 2` Find the distance between the point and the line.

The distance between a point and line will be measured by finding the segment that is perpendicular to the line and goes through the point. The formula to find this distance is: 


`"distance"(ax+by+c=0,(x1,y1))=|ax1+by1+c|/sqrt(a^2+b^2)`


So, in our problem, we need to set the equation of our line equal to 0, so it ends up being `3x+y-2=0`


We can now plug our numbers into the equation as follows:


`"distance"(3x+y-2=0,(-2,8))=|3(-2)+1(8)-2|/sqrt(3^2+1^2)`


Which leaves us with an answer of `0/sqrt(10)=0`


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