the question with the answers:

Attachment 24153

Attachment 24154

Attachment 24155

what i don't understand is this part:

Attachment 24156

how did that happen?

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- Jun 25th 2012, 01:52 AMmuddywatersperpendicular lines
the question with the answers:

Attachment 24153

Attachment 24154

Attachment 24155

what i don't understand is this part:

Attachment 24156

how did that happen? - Jun 25th 2012, 01:54 AMmuddywatersRe: perpendicular lines
click to enlarge :O

- Jun 26th 2012, 11:01 PMearbothRe: perpendicular lines
1. You know from equation 2:

$\displaystyle \displaystyle{y-y_0=-\frac1m(x-x_0)~\implies~(y-y_0)^2=\frac1{m^2}(x-x_0)^2}$

2. $\displaystyle \displaystyle{|\overline{PQ}|=\sqrt{(x-x_0)^2+(y-y_0)^2}}$

Replace $\displaystyle \displaystyle{(y-y_0)^2}$ by the term of #1:

$\displaystyle \displaystyle{|\overline{PQ}|=\sqrt{(x-x_0)^2+\frac1{m^2}(x-x_0)^2}}$

$\displaystyle \displaystyle{|\overline{PQ}|=\sqrt{\frac{m^2}{m^2 } (x-x_0)^2+\frac1{m^2}(x-x_0)^2}}$

Factor out $\displaystyle \displaystyle{(x-x_0)^2}$

$\displaystyle \displaystyle{|\overline{PQ}|=\sqrt{\frac{m^2-1}{m^2} (x-x_0)^2}}$ - Jun 26th 2012, 11:15 PMmuddywatersRe: perpendicular lines
yes. thanks :D