Download l1 : x - 5y + 11 = 0

MPM 2D
Unit #4
The Shortest Distance from the Origin to a Line
Example: Determine the shortest distance from the origin to the line
l1 : x - 5y + 11 = 0
Solution:
The shortest distance from a point to a line would be the
____________________ distance.
Step #1: Graph the given line and indicate the origin with its
l1 : x - 5y + 11 = 0
coordinates (0,0). Then, draw the line from the origin to the given line. It should be ______________________ to the given line. Where the lines meet call that point A.
Change the equation of the
line to y=mx+b form to graph.
m = _____ b = _____
Step #2: Find the equation of OA.
Need: 1. ___________
2. ___________
Therefore, the equation of OA is _____________________.
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Step #3: Solve the Linear System. We need to find the coordinates of point A (the point of intersection). We
can do this by solving the linear system mathematically by ____________
or ____________.
The equations of the lines are:
l1 : _________________
lOA : _________________
Therefore the coordinates of point A are ( ___ , ___ ).
.
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Step #4: Find the length of Line OA.
O ( ___, ___)
Using the length formula:
A ( ___, ___)
Therefore the shortest distance from the origin to the line
is approximately ______ units.
A quick way to remember the steps to find the shortest distance after you graph is:
E________________
S________________
L ________________
Homework: page 103 # 2 a,c,e
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