Question

the point (2,-3) is reflected across the x - axis. the image is then reflected across the line y = 4. what are the coordinates of the final image? (2,3) (-2,3) (2,7) (2,5)

Explanation:

Step1: Reflect across x - axis

When a point $(x,y)$ is reflected across the $x$-axis, the $x$-coordinate remains the same and the $y$-coordinate changes its sign. Given the point $(2, - 3)$, after reflection across the $x$-axis, the new point is $(2,3)$ since $x = 2$ and $y=-(-3)=3$.

Step2: Reflect across $y = 4$

The distance between the point $(2,3)$ and the line $y = 4$ is $d=4 - 3=1$. After reflection across the line $y = 4$, the $x$-coordinate remains $x = 2$, and the $y$-coordinate is $4+(4 - 3)=5$.

Answer:

$(2,5)$