Question

$A(1,-1)\text{and}{A}^{\prime }(-1,1)$ are plotted on the Cartesian plane. However, A' is incorrectly plotted. By how many units should A' be moved along the x-axis, such that A and A' are reflections of each other across the x-axis?

• A. 2 units upwards
  
• B. 2 units to the right
  
• C. 2 units to the left
  
• D. 2 units downwards
  

Answer 1

The correct option is B 2 units to the right


The points A and A' are reflections of each other across the y-axis. Since A' is plotted incorrectly, the coordinates of A are correct.

The coordinates of $A=(1,-1)$
Distance of A' from the y-axis =1 unit to the left
Distance of A' from the x-axis = 1 unit upwards

The coordinates of $A^{\prime }=(-1,1)$
Distance of A' from the y-axis = 1 unit to the left
Distance of A' from the x-axis = 1 unit upwards

Distance of its reflection A, from the y-axis must also be equal to the distance of A’ from the y-axis.
Distance of A from the y-axis as per the given coordinates = 1 unit to the right.
However, the distance of A from the y-axis to be a reflection of A' = Distance of A' from the y-axis (but to the right of the y-axis) = 4 unit to the right of the y-axis

Hence, the x-coordinate of $A=4$ in the right direction of the y-axis
The correct coordinates of $A=(4,1)$
The y-coordinates of both A and A' remain unchanged, as both are 1 unit above the x-axis.