Two sides of a parallelogram are along the lines, x + y = 3 & x -- y + 3 = 0.

Question

Two sides of a parallelogram are along the lines, x + y = 3 \& x -- y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is :

Accepted Answer

Solving

$$\begin{pmatrix} {x + y = 3}  \
   {x - y =  - 3}  \

\end{pmatrix} \,\, > \,\,A\left( {0,3} \right)$$

and  $${{{x_1} + 0} \over 2} = 2;\,\,{x_i} = 4$$

similarly y1 = 5

C  $$ \Rightarrow $$  (4, 5)

Now equation of BC is x - y = - 1

and equation of CD is x + y = 9

Solving x + y = 9  and  x - y = - 3

Point D is (3, 6)

Solutions · 1