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J & K CET Engineering J and K - CET Engineering Solved Paper-2015

  • question_answer
    Let A and B be points \[(8,\,\,10)\] and \[(18,\,20),\] respectively. If the point Q divides AB externally in the ratio \[2:3\] and M is the S mid-point of AB, then the length MQ is equal to

    A)  \[25\]                

    B)  \[5\sqrt{34}\]

    C)  \[25\sqrt{2}\]              

    D)   \[5\sqrt{26}\]

    Correct Answer: C

    Solution :

    Given points are \[A(8,\,\,10)\] and \[B(18,\,20)\]. M is the mid-point of AB. Coordinates of \[M=\left( \frac{8+18}{2}.\frac{10+20}{2} \right)=(13,15)\] Point Q divides AB externally in the ration of \[2:3\] Day The coordinates of Q \[=\left( \frac{2\times 18-3\times 8}{2-3},\,\frac{2\times 20-3\times 10}{2-3} \right)\] \[=\left( \frac{36-24}{-1},\frac{40-30}{-1} \right)\] \[=(-12,\,-10)\] Now, length \[MQ=\sqrt{{{(13+12)}^{2}}+{{(15+10)}^{2}}}\] \[\sqrt{{{(25)}^{2}}+{{(25)}^{2}}}\] \[\sqrt{2\times {{(25)}^{2}}}\] \[=25\sqrt{2}\]


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