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.

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the $y - axis$, the rule is $(x,y)\to(-x,y)$.

Step2: Assume original point coordinates

Let's assume the coordinates of the marked - point in the original figure are $(x,y)$. From the graph, if we assume the original point is $(5, - 2)$ (since it is 5 units to the right of the $y - axis$ and 2 units below the $x - axis$).

Step3: Apply reflection rule

Using the rule $(x,y)\to(-x,y)$, when $x = 5$ and $y=-2$, the new coordinates after reflection across the $y - axis$ are $(-5,-2)$.

Answer:

Point in original figure: $(5, - 2)$
Point in final figure: $(-5,-2)$