Name: Kat

Who is asking: Student
Level: Secondary

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:

  1. the shortest distance from a point P to a line L is the perpendicular distance.


  2. 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:

  1. 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.

  2. Write the equatiion of the line through P = (-2,-1) with slope -1/m. (This is the red line in the diagram.)

  3. Find the point Q where these two line intersect.

  4. Find the distance from P to Q.

I hope this helps,
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