A) 3
B) 5
C) \[3\sqrt{5}\]
D) \[5\sqrt{3}\]
Correct Answer: C
Solution :
We know that length of the line segment whose end point are \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] is \[d=\sqrt{({{y}_{2}}-{{y}_{1}})+{{({{x}_{2}}-{{x}_{1}})}^{2}}}\] Let \[(3,-1)=({{x}_{1}},{{y}_{1}})\] and \[(6,5)=({{x}_{2}},{{y}_{2}})\] \[\therefore \] \[d=\sqrt{({{y}_{2}}-{{y}_{1}})+{{({{x}_{2}}-{{x}_{1}})}^{2}}}\] \[=\sqrt{{{(6)}^{2}}+{{(3)}^{2}}}=\sqrt{36+9}\] \[=\sqrt{45}=\sqrt{9\times 5}=3\sqrt{5}\] So, length of the line segment whose end point are \[(3,-1)\] and \[(6,5)\] is \[3\sqrt{5}\].
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