Question

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

Explanation:

Step1: Recall reflection rule

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

Step2: Identify vertices of $\triangle FGH$

Let's assume the coordinates of $F=(x_1,y_1)$, $G=(x_2,y_2)$ and $H=(x_3,y_3)$.

Step3: Apply reflection rule to each vertex

For point $F=(x_1,y_1)$, its image $F'=(x_1,-y_1)$. For point $G=(x_2,y_2)$, its image $G'=(x_2,-y_2)$. For point $H=(x_3,y_3)$, its image $H'=(x_3,-y_3)$.

Step4: Plot the new triangle

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

Since the original coordinates of the vertices of $\triangle FGH$ are not given numerically, the general steps for graphing the reflection over the $x - axis$ are as above. To actually graph it, you would need to know the specific coordinates of the vertices of $\triangle FGH$ and then apply the $(x,y)\to(x, - y)$ rule to each vertex and plot the new points.

Answer:

Step1: Recall reflection rule

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

Step2: Identify vertices of $\triangle FGH$

Let's assume the coordinates of $F=(x_1,y_1)$, $G=(x_2,y_2)$ and $H=(x_3,y_3)$.

Step3: Apply reflection rule to each vertex

For point $F=(x_1,y_1)$, its image $F'=(x_1,-y_1)$. For point $G=(x_2,y_2)$, its image $G'=(x_2,-y_2)$. For point $H=(x_3,y_3)$, its image $H'=(x_3,-y_3)$.

Step4: Plot the new triangle

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

Since the original coordinates of the vertices of $\triangle FGH$ are not given numerically, the general steps for graphing the reflection over the $x - axis$ are as above. To actually graph it, you would need to know the specific coordinates of the vertices of $\triangle FGH$ and then apply the $(x,y)\to(x, - y)$ rule to each vertex and plot the new points.