SOLUTION: From the distance from (-4,-1) to the line defined by y=-2x+1. Express as a radical or a number rounded to the nearest hundredth.

Algebra ->  Length-and-distance -> SOLUTION: From the distance from (-4,-1) to the line defined by y=-2x+1. Express as a radical or a number rounded to the nearest hundredth.      Log On


   

Question 359558: From the distance from (-4,-1) to the line defined by y=-2x+1. Express as a radical or a number rounded to the nearest hundredth.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.y=-2x%2B1
The closest distance is formed by the line perpendicular to y=-2x%2B1 that goes through the point (-4,-1).
To find the perpendicular line, use the slope since perpendicular lines have slopes that are negative reciprocals.
m%5B1%5D%2Am%5B2%5D=-1
-2%2Am%5B2%5D=-1
m%5B2%5D=1%2F2
Now use the point slope form of a line, y-y%5Bp%5D=m%28x-x%5Bp%5D%29
y-%28-1%29=%281%2F2%29%28x-%28-4%29%29
y%2B1=%281%2F2%29%28x%2B4%29
2y%2B2=x%2B4
2.-x%2B2y=2
Now that you have both lines, find the intersection of the two lines.
The distance you're after is the distance from point (-4,-1) to the intersection point.
Substitute eq. 1 into eq. 2 and solve for x.
-x%2B2%28-2x%2B1%29=2
-x-4x%2B2=2
-5x=0
x=0
Then from eq. 1,
y=-2%280%29%2B1
y=1
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Now use the distance formula to find the distance from (-4,-1) to (0,1).
D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2
D%5E2=%280-%28-4%29%29%5E2%2B%281-%28-1%29%29%5E2
D%5E2=%284%29%5E2%2B%282%29%5E2
D%5E2=20
highlight%28D=2%2Asqrt%285%29%29 or approximately,
D=4.47