Thread: find the point

Find the point on the line which is closest to the point .

i know you have to find the distance and then the derivative of that but i got stuck when solving for d...

Actually, you don't need calculus for this question. You need to be cognizant of this basic fact.
The shortest line between a line ($\displaystyle l_1$) and a point (P) not on the line is the perpendicular line connecting $\displaystyle l_1$ and P.

So what you do is find the equation of the line perpendicular to the given line that goes through the point (-5,4), find where it intersects the original line and then use the length of a line formula.

Sketch the graph so you have a visual idea of what is going on.

if i use a perpendicular line equation, then wouldn't the intersecting point be the same as the original one they gave me? im not sure what they are asking since there are an infinite amount of points that could be considered the 'closest'