# Big test question

• Jan 16th 2006, 05:50 PM
Davey1
Big test question
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.
• Jan 16th 2006, 06:34 PM
jacs
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)

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

$
d = \frac{330}{\sqrt{37}} = 54.25
$
• Jan 16th 2006, 07:37 PM
ThePerfectHacker
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 $s=\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$.
• Jan 16th 2006, 07:43 PM
jacs
opps sorry, i forgot to include the forumla....