Sunday, June 12, 2011

`(-5, -3), -2x - 6y = 7` 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 `-2x-6y-7=0`


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


`"distance"(-2x-6y-7=0, (-5,-3))=|-2(-5)-6(-3)-7|/sqrt((-2)^2+(-5)^2)`


Which leaves us with an answer of `21/(2sqrt(10))~~3.32`


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