A) \[\text{QR}=S\text{P}\] and \[\text{PQ}=\text{RS}\]
B) \[\text{PQ}=\text{QR}\] and \[\text{RS}=S\text{P}\]
C) \[\text{PQ},\text{ QR},\text{ RS}\] and \[SP\] all are different
D) None of the above
Correct Answer: A
Solution :
| \[PQ=\sqrt{{{(4-7)}^{2}}+{{(5-6)}^{2}}}=\sqrt{{{(-3)}^{2}}+{{(-1)}^{2}}}=\sqrt{9+1}=\sqrt{10}\] |
| \[QR=\sqrt{{{(7-4)}^{2}}+{{(6-3)}^{2}}}=\sqrt{{{(3)}^{2}}+{{(3)}^{2}}}=\sqrt{9+9}=\sqrt{18}\] |
| \[RS=\sqrt{{{(4-1)}^{2}}+{{(3-2)}^{2}}}=\sqrt{{{(3)}^{2}}+{{(1)}^{2}}}=\sqrt{9+1}=\sqrt{10}\]and |
| \[PS=\sqrt{{{(4-1)}^{2}}+{{(5-2)}^{2}}}=\sqrt{{{(3)}^{2}}+{{(3)}^{2}}}=\sqrt{9+9}=\sqrt{18}\] |
| \[\therefore \,\,\,\,\,PQ=RS=\sqrt{10}\] and \[QR=PS=\sqrt{18}\] |
| So, option [a] is correct. |
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