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10th Class Mathematics Coordinate Geometry Question Bank Coordinate Geometry

  • question_answer
    Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter's school and then reaches the office. If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines)

    A)  \[2.2\text{ }km\]                  

    B) \[2.7\text{ }km\]            

    C)                     \[\text{11}\sqrt{3}\text{ }km\]         

    D)        \[2.40\text{ }km\]                         

    Correct Answer: D

    Solution :

    According to question, Distance covered from House to Bank \[=\sqrt{{{(5-2)}^{2}}+{{(8-4)}^{2}}}=\sqrt{9+16}=5\,km\] Distance covered from school to office \[=\sqrt{0+{{(26-14)}^{2}}}=12\,km\] \[\therefore \]  Total distance covered by Ayush \[=5+10+12=217\,km\] Also, Distance covered directly from House to office \[=\sqrt{{{(13-2)}^{2}}+{{(26-4)}^{2}}}=11\sqrt{5}km\] \[\therefore \]  Required distance \[=27-11\sqrt{5}=2.40\,km\]


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