SOLUTION: find the distance from (6,-4) to the line defined by y=2x-6

Question 749634: find the distance from (6,-4) to the line defined by y=2x-6
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
Typically we ask for the shortest distance because the distance from the line varies. So here we go...

There is a line perpendicular to our line that passes through (6,-4). Since it is perpendicular it has the slope -1/2

After some simplifying we can get

Notice that this new line must intersect our original at a point exactly parallel to (6,-4) (why?)

Therefore if we find the point of intersection we can use that point to find our distance

and this leads us to the x-coordinate which is x=2 and so y=2(2)-6=-2

Next we find the distance between (6,-4) and (2,-2)

and this gives us

Actually in precalculus there is a formula:

:)
RELATED QUESTIONS
Find the distance from (6,-1) to the line defined by y=2x-3. Please... (answered by Cromlix)

find the distance from (-6,-3) to the line defined by y=3x+5... (answered by josgarithmetic)

Find the distance from(2,-7) to the line defined by y=2x-6. Express as a radical or a... (answered by rfer)

Find the distance from (6,-3)to the line defined by y= 2x-5. Express as a radical or a... (answered by Alan3354,Fombitz,Edwin McCravy)

what is the distance from (-4,5) to the line defined by... (answered by dabanfield)

find the distance from (-6,-3) to the line defined by 3x+5. express as a radical or a... (answered by Alan3354)

From the distance from (-4,-1) to the line defined by y=-2x+1. Express as a radical or a... (answered by Fombitz)

find the distance from (6,5) to the line defined by y=-2x-8. express as radical or a... (answered by Alan3354)

find the distance from (2,1) to the line defined by y=-2x-5. Express as a radical or a... (answered by Alan3354)