A) (0, 13)
B) (0, -13)
C) (0, 12)
D) (13, 0)
Correct Answer: A
Solution :
Firstly, we plot the points of the line segment on the paper and join them. |
We know that, the perpendicular bisector of the line segment AB bisect the segment AB, i.e. perpendicular bisector of line segment AB passes through the mid-point of AB. |
\[\therefore\] Mid-point of \[AB=\left( \frac{1+4}{2},\,\frac{5+6}{2} \right)\] |
\[\Rightarrow \,\,\,P=\left( \frac{5}{2},\,\frac{11}{2} \right)\] |
[\[\because\] mid-point of line segment passes through the points \[\left( {{x}_{1}},\,{{y}_{1}} \right)\] and \[\left( {{x}_{2}},\,{{y}_{2}} \right)\] |
\[\left. =\left( \frac{{{x}_{1}}+{{x}_{2}}}{2},\frac{{{y}_{1}}+{{y}_{2}}}{2} \right) \right]\] |
Now, we draw a straight line on paper passes through the mid-point P. |
We see that the perpendicular bisector cuts the Y-axis at the point (0, 13). Hence, the required point is (0, 13). |
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