A) 9 or 6
B) 3 or -9
C) -3 or 9
D) 9 or -6
Correct Answer: B
Solution :
[b] Let \[A(2,-3)\]and \[B(10,y)\]be the end points of the line segment. |
\[\therefore \,\,\,\,\sqrt{{{(10-2)}^{2}}+{{(y+3)}^{2}}}=10\][\[AB=10\]units] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\sqrt{{{8}^{2}}+{{y}^{2}}+6y+9}=10\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\sqrt{{{y}^{2}}+6y+73}=10\] |
Squaring both sides, we get |
\[{{y}^{2}}+6y+73=100\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,{{y}^{2}}+6y-27=0\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,(y+9)\,\,(y-3)=0\] |
\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y=-9\] or 3 |
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