Bihar Police Constable Model Paper 5

GIVEN:
The vertices of the parallelogram = A(1, 2), B(a, -26), C(13, -14) and D(6, 14)
CONCEPT:
Using the distance formulae we will equate the parallel sides of the parallelogram.
FORMULAE USED:
D = $\sqrt{\left(\left({\mathit{x}}_2-{\mathit{x}}_1\right)\mathit{²}+\left({\mathit{y}}_2-{\mathit{y}}_1\right)\mathit{²}\right)}$
CALCULATION:
AB = DC
⇒ $\left\{{\left(\mathit{a}-1\right)}^2+{\left(-26-2\right)}^2\right\}$ = $\left\{{\left(6-13\right)}^2+{\left(14-\left(-14\right)\right)}^2\right\}$
⇒ ${\left(\mathit{a}-1\right)}^2$ + 784 = 49 + 784
⇒ ${\left(\mathit{a}-1\right)}^2$ = 49
⇒ a - 1 = 7
∴ a = 8