A coordinate plane is labeled with quadrants 1, 2, 3, and 4.

Question

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

Answer 1

To reflect a point across the x-axis, we change the sign of the y-coordinate while keeping the x-coordinate the same.

Point P is located at (-4, -7). When we reflect it across the x-axis, the new point P' will be:

P' = (x, -y) = (-4, 7).

Now we determine the quadrant for point P' = (-4, 7):

• The x-coordinate is -4 (which is negative).
• The y-coordinate is 7 (which is positive).

In the coordinate plane:

• Quadrant I has both coordinates positive (x > 0, y > 0).
• Quadrant II has a negative x-coordinate and a positive y-coordinate (x < 0, y > 0).
• Quadrant III has both coordinates negative (x < 0, y < 0).
• Quadrant IV has a positive x-coordinate and a negative y-coordinate (x > 0, y < 0).

Since P' has a negative x-coordinate and a positive y-coordinate, it is located in Quadrant II.

Therefore, the correct answer is Quadrant II.