Question

graph the image of △def after a reflection over the x - axis.

Explanation:

Step1: Recall reflection rule

The rule for reflecting a point $(x,y)$ over the $x - axis$ is $(x,-y)$.

Step2: Identify vertices of $\triangle DEF$

Let's assume the coordinates of the vertices of $\triangle DEF$ are $D(x_1,y_1)$, $E(x_2,y_2)$ and $F(x_3,y_3)$.

Step3: Apply reflection rule to each vertex

The new coordinates of $D$ after reflection over the $x - axis$ will be $D'(x_1,-y_1)$, for $E$ it will be $E'(x_2,-y_2)$ and for $F$ it will be $F'(x_3,-y_3)$.

Step4: Plot new triangle

Plot the points $D'$, $E'$ and $F'$ on the coordinate - plane and connect them to form the reflected triangle $\triangle D'E'F'$.

Since the original coordinates of $D$, $E$ and $F$ are not given numerically, we can't give exact numerical coordinates for the reflected points. But the general process is as above. If we assume $D(2, - 7)$, $E(7,-7)$ and $F(-3,-3)$:

Step1: Apply reflection rule to $D$

For $D(2,-7)$, the reflected point $D'(2,7)$ (using $(x,y)\to(x, - y)$).

Step2: Apply reflection rule to $E$

For $E(7,-7)$, the reflected point $E'(7,7)$.

Step3: Apply reflection rule to $F$

For $F(-3,-3)$, the reflected point $F'(-3,3)$.

Step4: Plot new triangle

Plot $D'(2,7)$, $E'(7,7)$ and $F'(-3,3)$ on the coordinate - plane and connect them to form $\triangle D'E'F'$.

Answer:

Plot the reflected vertices of $\triangle DEF$ using the rule $(x,y)\to(x, - y)$ and connect them to form the reflected triangle. If assuming $D(2,-7)$, $E(7,-7)$ and $F(-3,-3)$, plot $D'(2,7)$, $E'(7,7)$ and $F'(-3,3)$ and connect them.