question_answer

The perpendicular bisector of the line segment joining the points \[A\left( -2,\,-5 \right)\] and \[B\left( 4,\,6 \right)\]cuts the Y-axis at

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).