If the distance between the points \[(x,0)\]and \[(-7,0)\] be 10 units, then the possible values of x are [SSC (FCI) 2012] |
A) \[3\] and\[17\]
B) \[-\,\,3\]and \[17\]
C) \[3\] and \[-17\]
D) \[-\,\,3\]and \[-\,\,17\]
Correct Answer: C
Solution :
Distance between the point \[(x,0)\]and \[(-7,0)=10\] |
Given, \[{{x}_{1}}=x,\]\[{{y}_{1}}=0\] |
\[{{x}_{2}}=-\,\,7\] |
and \[{{y}_{2}}=0\] |
Required distance \[=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\] |
\[\Rightarrow \]\[10=\pm \,\,\sqrt{{{(-7-x)}^{2}}+{{(0-0)}^{2}}}\] |
\[\Rightarrow \]\[{{10}^{2}}=\pm \,\,{{(x+7)}^{2}}\] |
If \[x+7=10,\] |
Then, \[x=3\] |
If \[-\,\,(x+7)=10,\] |
Then, \[x=-\,\,17\] |
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