A) x = 6, y = 8
B) x = 2, y = 3
C) x = 6, y = 3
D) x = 5, y = 4
Correct Answer: C
Solution :
Let A (1, 2), B (4, y), C (x, 6) and D (3, 5) are the vertices of parallelogram. |
Since, ABCD is a parallelogram. |
\[\therefore \] AC and BD will bisect each other. Hence, mid- point of AC and mid-point of BD are same point. |
\[\therefore \]Mid-point of AC is \[\left( \frac{1+x}{2},\frac{2+6}{2} \right)\] |
= Mid-point of BD is\[\left( \frac{4+3}{2},\frac{y+5}{2} \right)\] |
\[\left[ \because \text{Mid-point}=\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right) \right]\] |
\[\therefore \] \[\frac{1+x}{2}=\frac{4+3}{2}\]and\[\frac{2+6}{2}=\frac{5+y}{2}\] |
\[\Rightarrow \] \[1+x=7\]and\[8=5+y\] |
\[x=6\]and\[y=3\] |
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