Notes: `(1, 1), y = x + 1` Find the distance between the point and the line.

Thursday, October 17, 2013

$\displaystyle{\left({1},{1}\right)},{y}={x}+{1}$ Find the distance between the point and the line.

Given (1, 1) $\displaystyle{y}={x}+{1}$

$\displaystyle{y}={x}+{1}$

$\displaystyle-{x}+{y}-{1}={0}$

Let A=-1, B=1, C=-1, x1=1, y1=1

Find the distance between the point and the line using the formula

$\displaystyle{d}=\frac{{\left|{A}{x}_{{1}}+{B}{y}_{{1}}+{C}\right|}}{\sqrt{{{{A}}^{{2}}+{{B}}^{{2}}}}}$

$\displaystyle{d}=\frac{{\left|{\left(-{1}\right)}{\left({1}\right)}+{\left({1}\right)}{\left({1}\right)}+{\left(-{1}\right)}\right|}}{\sqrt{{{{\left(-{1}\right)}}^{{2}}+{{1}}^{{2}}}}}$

$\displaystyle{d}=\frac{{\left|-{1}+{1}-{1}\right|}}{\sqrt{{{2}}}}=\frac{{1}}{\sqrt{{{2}}}}={.707}$

The distance between the point and the line is .707 units.

Notes

Thursday, October 17, 2013

$\displaystyle{\left({1},{1}\right)},{y}={x}+{1}$ Find the distance between the point and the line.

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