question_answer

A line segment is of length 10 units. If the coordinates of its end are  and the abscissa of the other end is 10, then its ordinate is:

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