Question

Point P(2,3) is a vertex of a rectangle. Determine the quadrant of P' if the rectangle is reflected across the x-axis. A. I B. II C. III D. IV

Answer 1

If you are reflecting across the x axis then the x coordinate will stay the same and the y coordinate will be negative. Draw a picture to help you see this.
That puts P prime in quadrant IV.

Answer 2

D. IV

Explanation:

If a point (x, y) reflected over the x-axis, then the x-coordinate remains the same and the sign of the y-coordinate will be changed.

x-axis

(x, y) -------> (x, -y)

We are given point P(2, 3) which is a vertex of a rectangle.

P' is the point which is reflected across the x-axis.

Therefore,

P (2, 3) -------------> P'(2, -3) is the reflected point across the x-axis.

Now we have to find in which the point P'(2, -3) lies.

There are four quadrants in a coordinate place. In the first quadrant (x, y) is always positive.

In the second quadrant, x-coordinate is negative and y-coordinate is positive. That is (-x, y)

In the third quadrant, x and y coordinates are negative. That is (-x, -y)

In the fourth quadrant, x-coordinate is positive and y-coordinate is negative. That is (x, -y)

Therefore, P'(2, -3) is in the IV quadrant.