Question

the figure below has a point marked with a large dot. first, reflect the figure across the y - 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: Identify original point coordinates

The marked point is 4 units left of the y-axis (x=-4) and 2 units above the x-axis (y=2). So original coordinates: $(-4, 2)$

Step2: Apply y-axis reflection rule

For reflection over the y-axis, the rule is $(x,y) \to (-x,y)$. Substitute $x=-4$, $y=2$:
$\text{New } x = -(-4) = 4$, $\text{New } y = 2$. So reflected coordinates: $(4, 2)$

Answer:

Point in original figure: $(-4, 2)$
Point in final figure: $(4, 2)$