Question

translate point x down 4 units and 9 units right. then, reflect the image over the x - axis. point x is the image of point x after the translation. now, reflect point x over the x - axis. original point image after translation and reflection x (-4,2) x

Explanation:

Step1: Perform the translation

For a point $(x,y)$ translated down $4$ units and $3$ units right, the new - $x$ coordinate is $x + 3$ and the new - $y$ coordinate is $y-4$. Given the original point $X(-4,2)$, the $x$ - coordinate of the translated point $X'$ is $-4 + 3=-1$, and the $y$ - coordinate is $2-4=-2$. So the point after translation is $(-1,-2)$.

Step2: Perform the reflection over the x - axis

When a point $(x,y)$ is reflected over the $x$ - axis, the $x$ - coordinate remains the same and the $y$ - coordinate changes its sign. For the point $(-1,-2)$ reflected over the $x$ - axis, the new point $X''$ has $x=-1$ and $y = 2$.

Answer:

$(-1,2)$