SOLUTION: Distance from a Point to a Line 6.Find the exact distance from the point D(4,-2) to the line segment joining the points E(1,3) and F(-4,-2). pleaseeee help me ...thank you ve

Question 189657: Distance from a Point to a Line
6.Find the exact distance from the point D(4,-2) to the line segment joining the points E(1,3) and F(-4,-2).

pleaseeee help me ...thank you very much!!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Distance from a Point to a Line
6.Find the exact distance from the point D(4,-2) to the line segment joining the points E(1,3) and F(-4,-2).
---------------
Step 1 - find the slope of the line
slope, m, = diffy/diffx = (-2-3)/(-4-1)
m = 1
--------------
Step 2 - find the equation of the line.
y-y1 = m*(x-x1) where (x1,y1) is either point (E or F)
y-3 = 1*(x-1)
y = x+2
-------
Step 3 - find the eqn of the line thru the point perpendicular to line EF. The shortest distance is on the line perpendicular.
The slope of lines perpendicular is the negative inverse of the slope of the line EF.
m2 = -1
use the method from Step 2
y-y1 = m*(x-x1) (x1,y1) is point D (4,-2)
y+2 = -1(x-4)
y = -x + 2
---------------
Step 4, find the point of intersection of the 2 lines
y = x+2
y = -x + 2
------------ Add
2y = 4
y = 2
x = 0
--> the point (0,2)
------
Last step, find the distance from D to (0,2)
s =
x =
x =
x =

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