LESSON 6 – SHORTEST DISTANCE FROM A POINT TO A LINE
Draw the path that gets Jolie to the water the fastest.
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 = 2𝑥 − 5.
STEP 1: Determine 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.
Example ②
a) Ms. Peleck is building a new cottage at map coordinates (3, 7). The beach lies between map
coordinates (−2, −1) and (5, −4). Ms. Peleck is cheap and lazy. Calculate the length of the
shortest path that connects her cottage to the beach? Units are measured in feet.
water
b) What is the cost of the path if Ms. Peleck would like to use Pattern Concrete at a cost of
$3.50/ sqft?