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

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(C) parallelogram is bounded by two pairs of parallel lines. Initially,there are $2$ parallel lines for each pair of sides. When $m$ lines are added p

Vedclass · Accepted Answer

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

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(C) parallelogram is bounded by two pairs of parallel lines. Initially,there are $2$ parallel lines for each pair of sides. When $m$ lines are added parallel to each side,the total number of parallel lines in each set becomes $m + 2$. To form a parallelogram,we need to select $2$ 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,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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