Big test question

Davey1 · January 16th 2006, 04:50 PM

Well, my math teacher gave us this question that he told us would be on the math test tomarow. Im not too sure how to do it but I have an idea.

An underground cable runs from (-20,35) to (-10,-25). Jessica's house is at (40,5). Determine the shortest distance of cable required to connect Jessys house and the underground cable.

So first what I did was get the slope of the underground wire.
M=(y2-y1)/(x2-x1). M=-25-35/-10-(-20) M=-6

Now i know the perp. bisector is 1/6.

Now i have to get the exuation of the line.
y=mx+b
y=5 x=40 m=1/6
When that was all done i got b=-1 1/3.

I dont know if that is right but this is where i am stuck at. It would be real great if someone could help me out. Thanks.

**jacs** · January 16th 2006, 05:34 PM

the equation of the line in general form for (-20, 35) (-10, -25) is

6x + y + 85 = 0

the shortest distance between a point and a line is the perpendicular distance

6x + y + 85 = 0 (40, 5)

$<br /> d= \frac{|6 * 40 + 1 * 5 + 85|}{\sqrt{6^2 +1^2}}<br />$

$<br /> d = \frac{330}{\sqrt{37}} = 54.25<br />$

**ThePerfectHacker** · January 16th 2006, 06:37 PM

Let me just help explain jacs answer.

If the equation of the a non-vertical line is $Ax+By+C$ (this is called standard form). And given a point $(x_0,y_0)$ Then the distance from the point to this line is $s=\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$ .

**jacs** · January 16th 2006, 06:43 PM

opps sorry, i forgot to include the forumla....

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