# Distance Expression

• Dec 28th 2007, 11:57 AM
lemon301
Distance Expression
Hey guys, I'm just needing a little help. Winter break definitely rusted up my brain.
What expression represents the distance from Point A (2,4) to Point C (10,d)?

I'm also needing help with this...

For what value of a is the line x + ay=26 parallel to the line 2x-4y=13?
• Dec 28th 2007, 12:42 PM
Plato
$d(P,Q) = \sqrt {\left( {x_P - x_Q } \right)^2 + \left( {y_P - y_Q } \right)^2 }$.

If we have a line $Ax + By + C = 0$ it has slope $\frac{{ - A}}{B}$.
Two parallel lines have the same slope.
• Jan 2nd 2008, 06:56 AM
lemon301
Quote:

Originally Posted by Plato
$d(P,Q) = \sqrt {\left( {x_P - x_Q } \right)^2 + \left( {y_P - y_Q } \right)^2 }$.

I'm sorry, I must just be really slow at this. How can I tell which is P and which is Q?
Would is be (2-4)^2 and (10-d)^2? Like 64 + 10d?
• Jan 2nd 2008, 07:11 AM
Isomorphism
Quote:

Originally Posted by lemon301
I'm sorry, I must just be really slow at this. How can I tell which is P and which is Q?
Would is be (2-4)^2 and (10-d)^2? Like 64 + 10d?

Ok now swap P and Q, then substitute in the formula and simplify...
The question is, does it matter which is which?
• Jan 2nd 2008, 07:12 AM
earboth
Quote:

Originally Posted by lemon301
I'm sorry, I must just be really slow at this. How can I tell which is P and which is Q?
Would is be (2-4)^2 and (10-d)^2? Like 64 + 10d?

Hi,

that doesn't matter because for instance

$(4-2)^2 = (2-4)^2$
• Jan 2nd 2008, 10:01 AM
lemon301
I'm trying to plug it in the formula you gave and so far I have (square root) 64 + d but should it be (square root) 64 + (d-4)^2?
• Jan 3rd 2008, 12:21 AM
JoFaSs
Quote:

Originally Posted by lemon301
I'm trying to plug it in the formula you gave and so far I have (square root) 64 + d but should it be (square root) 64 + (d-4)^2?

Yes,

$\sqrt{(d-4)^{2}+64}$