Question 1105948: A house is to be connected to a new water main
that runs along the line y=2/3x-1. The connection point at the house has coordinates(2,9), where the units represent meters. What exact length of plastic pipe is needed to connect to the water main at the closest point? (A diagram will help.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Want a line perpendicular to a line with slope 2/3, so that line will have slope -3/2, and it runs through point (2, 9). Point slope formula
y-y1=m(x-x1), m slope, (x1, y1) point
y-9=-(3/2)(x-2)
y-9=(-3x/2)+3
y=(-3x/2)+12
Now need to find the point of intersection.
(-3x/2)+12=(2/3)x-1
13=13x/6
x=6
y=-9+12=3
check in other equation
3=4-1, checks
The intersection point is at (6, 3)
Distance between (2, 9) and (6, 3) is sqrt ((6-2)^2+(3-9)^2)=sqrt (16+36)=sqrt(52) or 2 sqrt (13)
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