The coordinates $A (1, 1) and A^{'} (- 4, 1)$ 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?

3 units towards the right

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2 units towards the right

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3 units towards the left

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2 units towards the left

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Solution

The correct option is A 3 units towards 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 incorrect Point $A = (1, 1)$
Distance of incorrect A from the y-axis = 1 unit to the right
Distance of incorrect A from the x-axis = 1 unit upwards

The coordinates of $A^{'} = (- 4, 1)$
Distance of A' from the y-axis =4 units to the left
Distance of A' from the x-axis = 1 unit upwards

Distance of A and its reflection A’ must be equal from the y axis.
Distance of A' from the y-axis as per the given coordinates = 4 units to the left
So the distance of A from the y-axis should also be 4 units.

Hence, the x-coordinate of $A = 4$ units in the right direction of the y-axis
The correct coordinates of $A = (4, 1)$
So A should be moved 3 more units to the right to reach the correct coordinate position.
The y-coordinates of both A and A' remain unchanged, as both are 1 unit above the x-axis.
Hence, Option B is correct.

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The coordinates A(1,1) and A′(−4,1) 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?

The coordinates $A (1, 1) and A^{'} (- 4, 1)$ 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?