
Name: Kat
Who is asking: Student
Level: Secondary
Question:
Maybe one of you guys can help me with this, I'm really stuck. Find the shortest distance from the given line. Round to the nearest tenth. (2,1) and x+5y+20=0
Thanks a bunxh!
Hi Kat,
What you need to realize is that:
 the shortest distance from a point P to a line L is the perpendicular distance.
and

if a line has slope m then any line perpendicular to it has slope ^{1}/_{m}
To solve your problem you can proceed as follows:
 Solve the equation of line L: x + 5y + 20 = 0 for y to get an equation of the form y = mx + b. m is then the slope of L.
 Write the equatiion of the line through P = (2,1) with slope ^{1}/_{m}. (This is the red line in the diagram.)
 Find the point Q where these two line intersect.
 Find the distance from P to Q.
I hope this helps,
Penny
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