Question

The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and point A is reflected across the x-axis to obtain point C. What are the coordinates of points B and C?

B(2, 3) and, C(−2, −3)
B(−2, −3) and C(2, 3)
B(2, −3) and C(−2, 3)
B(−2, 3) and C(2, −3)

Answer 1

Answer: B(2, -3) and C(-2, 3) which is choice 3

Further Explanation:

The rule for a y-axis reflection is
`(\text{x}, \text{y}) \to (-\text{x}, \text{y})` meaning the x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.

Therefore, point A(-2,-3) moves to B(2, -3) when reflecting over the y-axis.

A similar rule is
`(\text{x}, \text{y}) \to (\text{x}, -\text{y})` to describe an x-axis reflection. This time the y coordinate flips in sign, and the x coordinate stays the same.

In this case, we move from A(-2,-3) to C(-2, 3)

The graph of all three points is shown below. I used GeoGebra to make the graph, but Desmos is another option. I also recommend graphing by hand on graph paper to get practice that way if possible.