SOLUTION: How can I find the distance from (2,-1) to the line y=1/2x+4 please answer soon!

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Question 374990: How can I find the distance from (2,-1) to the line y=1/2x+4
please answer soon!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The shortest distance between a line and a point is a line perpendicular to the first line going through the point.
Perpendicular lines have slopes that are negative reciprocals.
m%5B1%5D%2Am%5B2%5D=-1
%281%2F2%29%2Am%5B2%5D=-1
m%5B2%5D=-2
Then use the slope-intercept form of a line,
y=mx%2Bb
y=-2x%2Bb
Use the point to solve for b.
-1=-2%282%29%2Bb
b=-1%2B4
b=3
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y=-2x%2B3
Find the intersection point between the two lines.
-2x%2B3=%281%2F2%29x%2B4
-%285%2F2%29x=1
x=-2%2F5
Then,
y=-2%28-2%2F5%29%2B3
y=4%2F5%2B3
y=19%2F5
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Use the distance formula to find the distance from (2,-1) to (-2%2F5,19%2F5).
D%5E2=%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2
D%5E2=%28-2%2F5-2%29%5E2%2B%2819%2F5-%28-1%29%29%5E2
D%5E2=%28-2%2F5-10%2F5%29%5E2%2B%2819%2F5%2B5%2F5%29%5E2
D%5E2=%28-12%2F5%29%5E2%2B%2824%2F5%29%5E2
D%5E2=%28144%2F25%29%2B%28576%2F5%29
D%5E2=720%2F25
highlight%28D=%2812%2F5%29%2Asqrt%285%29%29
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