Question
A four-sided figure W(quadrant II), X(quadrant III), Y(quadrant IV), Z(quadrant I) is shown on the coordinate plane. The figure is then reflected across the x-axis. Which point of the figure will end up in quadrant I.
Answers
GPT-4o mini
To determine which point of the four-sided figure will end up in quadrant I after being reflected across the x-axis, we need to analyze the coordinates of each point in relation to each quadrant.
1. **Point W** is in quadrant II: In this quadrant, the x-coordinates are negative, and the y-coordinates are positive (e.g., W(x, y) where x < 0 and y > 0). When reflected across the x-axis, the y-coordinate changes sign, so W will move to quadrant III.
2. **Point X** is in quadrant III: In this quadrant, both x-coordinates and y-coordinates are negative (e.g., X(x, y) where x < 0 and y < 0). After reflection across the x-axis, the y-coordinate becomes positive, moving X to quadrant II.
3. **Point Y** is in quadrant IV: In this quadrant, the x-coordinates are positive, and the y-coordinates are negative (e.g., Y(x, y) where x > 0 and y < 0). When reflected across the x-axis, Y's y-coordinate will change to positive, moving Y to quadrant I.
4. **Point Z** is in quadrant I: In this quadrant, both x-coordinates and y-coordinates are positive (e.g., Z(x, y) where x > 0 and y > 0). Reflecting Z across the x-axis will change the y-coordinate to negative, moving Z to quadrant IV.
From the analysis above, **point Y**, which is originally in quadrant IV, will end up in quadrant I after being reflected across the x-axis.
1. **Point W** is in quadrant II: In this quadrant, the x-coordinates are negative, and the y-coordinates are positive (e.g., W(x, y) where x < 0 and y > 0). When reflected across the x-axis, the y-coordinate changes sign, so W will move to quadrant III.
2. **Point X** is in quadrant III: In this quadrant, both x-coordinates and y-coordinates are negative (e.g., X(x, y) where x < 0 and y < 0). After reflection across the x-axis, the y-coordinate becomes positive, moving X to quadrant II.
3. **Point Y** is in quadrant IV: In this quadrant, the x-coordinates are positive, and the y-coordinates are negative (e.g., Y(x, y) where x > 0 and y < 0). When reflected across the x-axis, Y's y-coordinate will change to positive, moving Y to quadrant I.
4. **Point Z** is in quadrant I: In this quadrant, both x-coordinates and y-coordinates are positive (e.g., Z(x, y) where x > 0 and y > 0). Reflecting Z across the x-axis will change the y-coordinate to negative, moving Z to quadrant IV.
From the analysis above, **point Y**, which is originally in quadrant IV, will end up in quadrant I after being reflected across the x-axis.