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  • A triangle ABC lying in the first quadrant has two vertices as A (1,2) and B(3,1). If  , and ar <img alt="(

A triangle ABC lying in the first quadrant has two vertices as A (1,2) and B(3,1). If \angle BAC = 90^{\circ} , and ar (\Delta ABC)= 5 \sqrt{5} sq. units, then the abscissa of vertex C is:
Option: 1 1 +\sqrt{5}
Option: 2 1 +2\sqrt{5}
Option: 3 2+\sqrt{5}
Option: 4 2\sqrt{5}-1

Answers (1)

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\begin{aligned} &\left(\frac{\mathrm{K}-2}{\mathrm{~h}-1}\right)\left(\frac{1-2}{3-1}\right)=-1 \Rightarrow \mathrm{K}=2 \mathrm{~h}\\ &\sqrt{5}|\mathrm{~h}-1|=10\\ &\because[\Delta \mathrm{ABC}]=5 \sqrt{5}\\ &\Rightarrow \frac{1}{2}(\sqrt{5}) \sqrt{(\mathrm{h}-1)^{2}+(\mathrm{K}-2)^{2}}=5 \sqrt{5}\\ &\Rightarrow \mathrm{h}=2 \sqrt{5}+1(\mathrm{~h}>0) \end{aligned}

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himanshu.meshram

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