##### Quadrilateral BCDE is a square.

label Algebra
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Oct 22nd, 2017

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Coordinates of B are B(0, 3) and

coordinates of C are C(3, 5)

Slope of BC

$\\ =\frac{y_2-y_1}{x_2-x_1}\\ \\ =\frac{5-3}{3-0}\\ \\ =\frac{2}{3}\\$

Since BCDE is a square, BC || DE .

If two lines are parallel, then they have the same slope.

So, slope of DE $=\frac{2}{3}\\$

Since BCDE is a square, $BC\perp EB$ and $BC\perp CD$ .

If two lines are perpendicular, then product of their slopes is equal to -1.

Let slope of EB and CD be m.

So,

$\\ m\times\frac{2}{3}=-1\\ \\ m=-\frac{3}{2}$

Hence, slope of CD = slope of EB = $m=-\frac{3}{2}$

ANSWER: D)   BC $=\frac{2}{3}\\$ , CD = $-\frac{3}{2}$ , DE $=\frac{2}{3}\\$, EB = $-\frac{3}{2}$

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 27th, 2015

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Oct 22nd, 2017
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Oct 22nd, 2017
Oct 23rd, 2017
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