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The vertices of a parallelogram $ABCD$ are $A (3, 1), B (13, 6), C (13, 21)$ and $D (3, 16)$ . If a line passing through the origin divides the parallelogram into two congruent parts, then the slope of the line is

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11/8

11/12

13/8

25/8

answer is B.

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Detailed Solution

Slope of line through origin is,

$m = \frac{21 - x}{13} = \frac{x + 1}{3}$

or $63 - 3 x = 13 x + 13$

or $16 x = 50$

or $x = \frac{25}{8}$

Hence, $m = (\frac{25}{8} + 1) \times \frac{1}{3}$

$= \frac{33}{24} = \frac{11}{8}$

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