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: (-6, point in final figure: (-6, 2)

Explanation:

Step1: Identify original point

The marked point on the upper triangle has an x-coordinate of -6 and a y-coordinate of 3. So original point: $(-6, 3)$

Step2: Apply x-axis reflection rule

Reflecting a point $(x, y)$ across the x-axis changes the sign of the y-coordinate, using the formula $(x, y) \to (x, -y)$.
Substitute $x=-6$, $y=3$: $(-6, -3)$? No, correction: Wait, the pre-filled final figure has a typo. Correct reflection: $(-6, 3) \to (-6, -3)$? No, wait the lower figure is the reflection. Wait no, original marked point is at $(-6, 3)$. Reflect over x-axis: flip y-sign.

(Revised):

Step1: Locate original marked point

Read coordinates from grid: $(-6, 3)$

Step2: Apply reflection transformation

Rule for x-axis reflection: $(x,y)\to(x,-y)$
Substitute values: $(-6, 3)\to(-6, -3)$

Answer:

Point in original figure: $(-6, 3)$
Point in final figure: $(-6, -3)$

Wait, correction: Looking at the grid, the original marked point is at x=-6, y=3. Reflecting across x-axis (y=0) gives y=-3, so final point is $(-6, -3)$. The pre-filled $(-6,2)$ is incorrect. The correct coordinates are:
Original: $(-6, 3)$
Final (reflected): $(-6, -3)$