Question

(a) the arrows below show that the coordinates on the left are mapped to the coordinates on the right. fill in the boxes original coordinates → final coordinates d(-8, -4)→d(-8, 4) e(2, -3)→e(2, 3) f(-5, -7)→f(-5, 7) (b) choose the general rule below that describes the reflection mapping △def to △def. (x,y)→(-x,y) (x,y)→(-y,x) (x,y)→(x, -y) (x,y)→(y, -x)

Explanation:

Step1: Analyze the change in coordinates for reflection

For a point $(x,y)$ reflected over the $x -$axis, the $x$-coordinate remains the same and the $y$-coordinate changes sign, i.e., $(x,y)\to(x, - y)$. For a reflection over the $y$-axis, the $y$-coordinate remains the same and the $x$-coordinate changes sign, i.e., $(x,y)\to(-x,y)$.
Let's check the given coordinate - pairs:
For point $D(-8,-4)\to D'(-8,4)$, the $x$-coordinate remains $- 8$ and the $y$-coordinate changes from $-4$ to $4$. This is a reflection over the $x$-axis.
For point $E(2,-3)\to E'(2,3)$, the $x$-coordinate remains $2$ and the $y$-coordinate changes from $-3$ to $3$. This is a reflection over the $x$-axis.
For point $F(-5,-7)\to F'(-5,7)$, the $x$-coordinate remains $-5$ and the $y$-coordinate changes from $-7$ to $7$. This is a reflection over the $x$-axis.
The general rule for a reflection over the $x$-axis is $(x,y)\to(x,-y)$.

Answer:

$(x,y)\to(x, - y)$