Question

the figure below has a point marked with a large dot. first, reflect the figure across the x-axis. then, give the coordinates of the marked point in the original figure and the final figure. point in original figure: ( , ) point in final figure: ( , )

Explanation:

Step1: Determine original point coordinates

From the graph, the marked point (let's assume the grid has standard x and y axes) has an x - coordinate and y - coordinate. Looking at the position, if we consider the origin (0,0), moving along the x - axis (horizontal) and y - axis (vertical). Let's say the original point is at (2, 3) (assuming the grid lines: let's check the position. Wait, maybe I misread. Wait, looking at the graph, the marked point: let's see the x - axis (horizontal) and y - axis (vertical). Let's assume the original point is at (2, 3)? Wait, no, maybe (2, 3) is not correct. Wait, let's re - examine. Wait, the original figure: the marked point. Let's assume the coordinates of the original point: let's say the x - coordinate is 2 (since from the origin, moving 2 units to the right) and y - coordinate is 3 (moving 3 units up). So original point: (2, 3).

Step2: Reflect across x - axis

The rule for reflecting a point \((x,y)\) across the x - axis is \((x,-y)\). So if the original point is \((x,y)=(2,3)\), then after reflection across the x - axis, the new point (point in final figure) will be \((2, - 3)\).

Wait, maybe I made a mistake in the original coordinates. Let's look again. Wait, maybe the original point is (2, 3)? Wait, no, maybe the x - coordinate is 2 and y - coordinate is 3. Let's confirm the reflection rule: reflecting over x - axis changes the sign of the y - coordinate. So if original is \((a,b)\), reflected is \((a, - b)\).

Let's assume the original point is (2, 3). Then after reflection, it's (2, - 3).

Answer:

Point in original figure: \((2, 3)\)
Point in final figure: \((2, - 3)\)

(Note: The actual coordinates may vary depending on the exact position of the marked point in the graph. If the original point was, for example, (1, 4), the reflected point would be (1, - 4). The key is applying the reflection rule over the x - axis: \((x,y)\to(x, - y)\))