Use the image to answer the question. The point (2, −3) is reflected across the x-axis. In what quadrant is the reflected point located? Quadrant $$
The reflection across the x-axis changes the sign of the y-coordinate, but leaves the x-coordinate unchanged.
The original point (2, -3) has a negative y-coordinate, which means it is located in the fourth quadrant.
When the point is reflected across the x-axis, the new y-coordinate becomes positive, so the reflected point is located in the first quadrant.
To determine the quadrant where the reflected point is located, we need to consider the signs of the coordinates.
In the given point (2, -3), the x-coordinate is positive (2) and the y-coordinate is negative (-3).
When a point is reflected across the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate changes.
Therefore, when we reflect the point (2, -3) across the x-axis, the x-coordinate will still be positive (2), but the sign of the y-coordinate will change.
Since the original y-coordinate is negative (-3) and it changes to positive when reflected, we can say that the reflected point is located in the
- First Quadrant.
To determine in which quadrant the reflected point is located, we need to analyze the changes that occur when a point is reflected across the x-axis.
When a point is reflected across the x-axis, the y-coordinate of the original point is negated, while the x-coordinate remains the same. So, if a point has positive y-coordinate, after reflecting across the x-axis, the reflected point will have a negative y-coordinate.
In the given question, the original point is (2, -3). Since the original y-coordinate is already negative (-3), when we reflect it across the x-axis, the y-coordinate becomes positive. Therefore, the reflected point should have positive y-coordinate.
Based on this analysis, we can conclude that the reflected point will be located in either the second quadrant or the first quadrant.
However, to be certain, we need to consider the original x-coordinate. In this case, the x-coordinate of the original point is 2. Since it is positive, the x-coordinate will remain positive after reflection across the x-axis.
Combining the information, we can determine that the reflected point (2, -3) across the x-axis will be in the second quadrant.