Question

The reflection of \[{\text{( - 6, - 3)}}\]on the y-axis has coordinates
a. \[{\text{( - 6,3)}}\]
b. \[{\text{(6, - 3)}}\]
c. \[{\text{(6,3)}}\]
d. \[{\text{( - 3,6)}}\]

Answer 1

Hint: To find reflection of a point with coordinate \[{\text{(x,y)}}\]with respect to y-axis we just negate the value of x coordinate, i.e. \[{\text{( - x,y)}}\]. So if we are to find the reflection of a point, we need to think that a point is placed in front of a mirror and how it would look in the mirror.

Complete step by step Answer:

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed i.e. its sign is changed.

Notice that if B is 5 horizontal units to the right of the y-axis, and B' is 5 horizontal units to the left of the y-axis.
Given point\[{\text{( - 6, - 3)}}\],
The reflection of the point\[{\text{(x,y)}}\]across the y-axis is the point\[{\text{( - x,y)}}\].
So, we have, our point of reflection as, \[{\text{(6, - 3)}}\].
Hence, the correct option is an option (B).

Note: If we need to find reflection by the x-axis, then we will have a different answer. In this case, the sign of the y coordinate would change. Example here if we find reflection with respect to the x-axis, that will be, \[{\text{( - 6,3)}}\] as a point of reflection. You must read the question carefully and find the reflection of the point with respect to the given axis only.