UNIT 2 – ANALYTIC GEOMETRY
(Lesson 6 – Shortest Distance from a Point to a Line)
The shortest distance is always the perpendicular distance from the point to
the line.
Example 1: Determine shortest distance from the origin, A(0, 0), to the line y  2 x  5 .
The shortest distance is the perpendicular distance AB, where B is the point on the line.
 need to find the coordinates of point B.
STEP 1: Determine the equation of AB
a) Calculate the slope of AB
b) Use the given point on AB
c) Write the equation of AB
STEP 2: Determine the coordinates of B by solving for the point of intersection of the two
lines.
STEP 3: Calculate the length of AB using lab  ( x2  x1 ) 2  ( y 2  y1 ) 2
Example 2: Ms. DiIorio is building a new home at map coordinates (3, 7). A road already
exists between her two best friends’ homes at (-2, -1) and (5, -4). Ms. DiIorio is cheap and lazy.
What would be the shortest route to build a road to connect to her friends? Determine the
length of the road in kilometers?