Questions: Point P is located at (-4,-7). P is reflected across the x-axis to create P'. In which quadrant is P' located? Quadrant I Quadrant II Quadrant III Quadrant IV

Solution Steps

Reflecting a point across the \( x \)-axis changes the sign of the \( y \)-coordinate while keeping the \( x \)-coordinate the same. Mathematically, if a point \( P(x, y) \) is reflected across the \( x \)-axis, the new point \( P' \) will have coordinates \( (x, -y) \).

Given the original point \( P(-4, -7) \), reflecting it across the \( x \)-axis changes the \( y \)-coordinate from \(-7\) to \(7\). Thus, the coordinates of \( P' \) are: \[ P'(-4, 7) \]

The point \( P'(-4, 7) \) has a negative \( x \)-coordinate and a positive \( y \)-coordinate. According to the quadrant definitions:

• Quadrant I: \( x > 0 \), \( y > 0 \)
• Quadrant II: \( x < 0 \), \( y > 0 \)
• Quadrant III: \( x < 0 \), \( y < 0 \)
• Quadrant IV: \( x > 0 \), \( y < 0 \)

Since \( P'(-4, 7) \) has \( x < 0 \) and \( y > 0 \), it lies in Quadrant II.

Final Answer