Question

$A(1,-1)\text{and}{A}^{\prime }(-2,1)$ 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 y-axis?

• A. 3 units upwards
  
• B. 2 units to the left
  
• C. 3 units to the left
  
• D. 2 units downwards
  

Answer 1

The correct option is C 3 units to the left



The coordinates of $A^{\prime }=(-2,1)$
The reflected point $(-2,-1)$ will be in the third quadrant with coordinates (-x, -y).
The reflection of point A' along the x-axis $=A^{\prime }(-2,-1)$
Given that the coordinates of $A=(1,-1)$

Distance of A’ from the y-axis towards left $=2\text{unit}$
Distance of A’ from the x-axis upwards$=1\text{unit}$
Distance of A and its reflection A' from the x-axis must also be equal.
So the distance of $A(1,-1)$ from the y-axis $=1\text{unit}$
Therefore, the y-coordinates of both A and A’ remain unchanged, as both are 1 unit below the x-axis.
However, the x-coordinate should be moved 3 units to the left from the current position.