| If the point A (6, 1), B (8, 2), C (9, 4) and D (p, 3) are the vertices of a parallelogram taken in order, find the value of p. |
A) 3
B) 4
C) 5
D) 6
E) 7
Correct Answer: E
Solution :
| Diagonal of a parallelogram bisect each other. |
| So, the coordinate of mid-point of AC = coordinate or mid-point of BD |
| \[\Rightarrow \]\[\left( \frac{6+9}{2},\frac{1+4}{2} \right)=\left( \frac{8+P}{2},\frac{2+3}{2} \right)\] |
| \[\left( \frac{15}{2},\frac{5}{2} \right)=\left( \frac{8+P}{2},\frac{5}{2} \right)\] |
| On comparing, \[\frac{8+P}{2}=\frac{15}{2}\] |
| \[\Rightarrow \] \[16+2p=30\] |
| \[\Rightarrow \] \[2p=30-16\] |
| \[\Rightarrow \] \[2P=14\]\[\Rightarrow \]\[P=7\] |
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