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If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
Answer :



Mid point of AC = Mid point BD
\(\Rightarrow \frac{x+1}{2} , \frac{6+2}{2} = \frac{4+3}{2} , \frac{y+5}{2} \)
\(\Rightarrow \frac{x+1}{2} = \frac{7}{2} \)
\(\Rightarrow x +1 = 7 \)
\(\Rightarrow x = 7-1= 6 \)
\(\Rightarrow \frac{y+5}{2} = \frac{8}{2} \)
\(\Rightarrow y+5 = 8 \)
\(\Rightarrow y = 8 -5 = 3 \)