Coordinate geometry - Line equation

SOURCE:COMPETITION
Number of Problems: 6. : (Book)

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Define $aclubsuit b=a^2b-ab^2$ . Which of the following describes the set of points $(x, y)$ for which $xclubsuit y=yclubsuit x$ ?

$extbf{(A)} ext{a finite set of points}\ qquad extbf{(B)} ext{one line}\ qquad extbf{(C)} ext{two parallel li...$

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4.

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The diagram shows $28$ lattice points, each one unit from its nearest neighbors. Segment $AB$ meets segment $CD$ at $E$ . Find the length of segment $AE$ .

$mathrm{(A)} frac{4sqrt{5}}{3} qquadmathrm{(B)} frac{5sqrt{5}}{3} qquadmathrm{(C)} frac{12sqrt{5}}{7} qquadmat...$

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5.

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A line with slope $3$ intersects a line with slope $5$ at point $(10,15)$ . What is the distance between the $x$ -intercepts of these two lines?

$extbf{(A) } 2 qquad extbf{(B) } 5 qquad extbf{(C) } 7 qquad extbf{(D) } 12 qquad extbf{(E) } 20$

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6.

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In rectangle $ABCD$ , we have $A=(6,-22)$ , $B=(2006,178)$ , $D=(8,y)$ , for some integer $y$ . What is the area of rectangle $ABCD$ ?

$mathrm{(A) } 4000qquad mathrm{(B) } 4040qquad mathrm{(C) } 4400qquad mathrm{(D) } 40,000qquad mathrm{(E) }...$

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