A parallelogram is cut by two sets of m lines | vedclass

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(C) parallelogram is defined by two pairs of parallel lines. Initially,the parallelogram has $2$ sides in each direction. When $m$ lines are added par

Vedclass · Accepted Answer

$({^{m+2}C_2})^2$

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(C) parallelogram is defined by two pairs of parallel lines. Initially,the parallelogram has $2$ sides in each direction. When $m$ lines are added parallel to each set of sides,each set now contains $m + 2$ parallel lines. $A$ parallelogram is formed by selecting $2$ lines from the first set of $m + 2$ lines and $2$ lines from the second set of $m + 2$ lines. The number of ways to choose $2$ lines from $m + 2$ lines is given by $^{m+2}C_2$. Since we need to choose from both sets independently,the total number of parallelograms is $^{m+2}C_2 	imes {^{m+2}C_2} = ({^{m+2}C_2})^2$.

$A$ parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is

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