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The perpendicular bisector of the line segment joining the points $7 + 7i$ and $7 - 7i$ in the Argand diagram has the equation:
A.$y = 0$
B.$x = 0$
C.$y = x$
D.$x + y = 0$

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Last updated date: 20th Jun 2024
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Answer
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Hint: We will use the graphical method to solve for the equation of the perpendicular bisector of the line segment which joins the points $7 + 7i$ and $7 - 7i$. We will plot these two points on the Argand plane and then by observation, we will find the perpendicular bisector of the line segment which joins these two points.

Complete step-by-step answer:
We are given two points $7 + 7i$ and $7 - 7i$. It is given that a line segment joins these two points.
We are required to find the equation of the perpendicular bisector of the line segment joining the two points.
The Argand diagram is defined as a diagram in which complex numbers are represented by points in the plane and the coordinates of which re respectively the real and the imaginary parts of the complex number i.e., the complex number $x + iy$ will be represented by the point $\left( {x,y} \right)$.
We can plot the points $7 + 7i$ and $7 - 7i$ on the Argand plane as:
seo images

Let AB be the line segment joining the points $7 + 7i$ and $7 - 7i$. We need to calculate the perpendicular bisector of AB.
Now, if we look at the graph, we can see that the perpendicular bisector of the line AB will be the x – axis itself.
We know the equation of the x – axis is $y = 0$ since every y – coordinate on the x – axis is 0.
Therefore, the equation of the perpendicular bisector of the line segment joining the point $7 + 7i$ and $7 - 7i$ is $y = 0$.
Hence, option (A) is correct.

Note: In this question, you may go wrong in plotting the points on the Argand plane and hence in determining the correct equation of the perpendicular bisector. In mathematics, the Argand plane (or complex plane) is a graphical (or geometrical) representation of the complex numbers. Any complex number $z = x + iy$ will be denoted by $\left( {x,y} \right)$ where x is the real part and y is the imaginary part of the complex number.