Distance to Line/Point on Coordinate Plane- please help!

Please note that it's highly unlikely that you'll need this for GMAT.

DISTANCE BETWEEN THE LINE AND POINT:
Line: \(ay+bx+c=0\), point \((x_1,y_1)\)

\(d=\frac{|ay_1+bx_1+c|}{\sqrt{a^2+b^2}}\)

DISTANCE BETWEEN THE LINE AND ORIGIN:
As origin is \((0,0)\) -->

\(d=\frac{|c|}{\sqrt{a^2+b^2}}\)

Question about "THE DISTANCE BETWEEN THE CIRCLE AND THE LINE": tough-tricky-set-of-problms-85211.html#p638361 There are two solutions for this problem, one uses the formula above and another right triangle properties and basics of coordinate geometry.

Hope it helps.

I'd point out that while I've seen the occasional prep company question that asks about distances from points to lines, I've never, in ten years in this field, seen a real GMAT question that does. So while memorizing formulas like the one in the posts above might help you on a high school coordinate geometry test, it is extremely unlikely to make any difference on the GMAT.

And if you were given some point (a, b) and some line y = mx + c, and asked to find the perpendicular distance from (a,b) to the line, you could always:

* find the equation of the line perpendicular to y = mx + c which contains (a,b). That line has a slope of -1/m, and you can find its y-intercept by plugging in the point

* now find where the first line and its perpendicular intersect by solving the two equations together - that will be at some point (d,e)

* find the distance from (d,e) to (a,b) to get the answer

Following those steps, you can derive the formula in the posts above. You may well need to do one of the three things above in a question, but you're very unlikely to need to do all three, so I think it's vastly preferable to learn each concept individually rather than memorizing formulas that you'll most likely never have occasion to use.

Ian, I had this question on my Real GMAT last month. Of course, there could have some back-solving way, but I have not seen such and numbers were ugly.

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