question_answer

In triangle \[ABC,\angle A={{90}^{o}}\]and \[AB=AC\]and the coordinate of B and C are (-3, 6) and (1,2) respectively, then the area of triangle is:

A)  4 sq unit

B)                        \[4\sqrt{2}\,\]sq unit

C)                         8 sq unit             

D)         \[\left( -\frac{1}{5},-\frac{22}{5} \right)\]

Correct Answer: C

Solution :

Given that coordinate of \[B(-3,6)\]and C (1, 2). \[\therefore \]  \[BC=\sqrt{{{4}^{2}}+{{(-4)}^{2}}}\]                                 \[=4\sqrt{2}\] Since, \[AB=AC\]\[\Rightarrow \]\[\angle B=\angle C={{45}^{o}}\] In \[\Delta ABC,\] \[\cos ={{45}^{o}}=\frac{AB}{BC}\] \[\Rightarrow \]               \[AB=4\sqrt{2}.\frac{1}{\sqrt{2}}\] \[\Rightarrow \]               \[AB=AC=4\] \[\therefore \] Area of triangle \[=\frac{1}{2}\times BA\times AC\]                                 \[=\frac{1}{2}\times 4\times 4\]                                 \[=8\,\text{q}\,\text{unit}\]