Question

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

(a)  13/8

(b)  11/12

(c)  8/11

(d)  11/8

Answer 1

Correct option (d)  11/8

Explanation :

See Fig.  It can be observed that AD and BC are vertical lines. Suppose the line through the origin meets AD at P and BC at Q in such a way that CQ = PA, DP = BQ. Also PQCD and PQBA are the congruent parts. Suppose AP = k.

Therefore, P = (3, k + 1) Q = (13,21 - k) .

 Hence, the slope of the line is 

Thus, the slope of the line is

= (25/8) + 1/3 = 33/3 x 8 = 11/8