3.10. Distance Formula in the Coordinate Plane http://www.ck12.org
First, graph the line and point. Second determine the equation of the perpendicular line. The opposite sign and
reciprocal of^13 is -3, so that is the slope. We know the line must go through the given point, (1, 5), so use that to find
they−intercept.
y=− 3 x+b
5 =− 3 ( 1 )+b The equation of the line isy=− 3 x+ 8.
8 =bNext, we need to find the point of intersection of these two lines. By graphing them on the same axes, we can see
that the point of intersection is (3, -1), the green point.
Finally, plug (1, 5) and (3,-1) into the distance formula to find the shortest distance.