Question

7 directions - reflect the triangle according to the rules: a) reflect △abc over the x - axis. b) then, reflect △abc over the y - axis.

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point $(x,y)$ over the x - axis is $(x,-y)$. Let the vertices of $\triangle ABC$ be $A(x_1,y_1)$, $B(x_2,y_2)$ and $C(x_3,y_3)$. After reflection over the x - axis, the vertices of $\triangle A'B'C'$ are $A'(x_1, - y_1)$, $B'(x_2,-y_2)$ and $C'(x_3,-y_3)$.

Step2: Recall reflection over y - axis rule

The rule for reflecting a point $(x,y)$ over the y - axis is $(-x,y)$. After reflecting $\triangle A'B'C'$ over the y - axis, if the vertices of $\triangle A'B'C'$ are $A'(x_1, - y_1)$, $B'(x_2,-y_2)$ and $C'(x_3,-y_3)$, the vertices of the final triangle $\triangle A''B''C''$ are $A''(-x_1,-y_1)$, $B''(-x_2,-y_2)$ and $C''(-x_3,-y_3)$.

Answer:

To find the final reflected triangle, first apply the $(x,y)\to(x, - y)$ rule to each vertex of $\triangle ABC$ to get $\triangle A'B'C'$, and then apply the $(x,y)\to(-x,y)$ rule to each vertex of $\triangle A'B'C'$ to get the final reflected triangle. Without the actual coordinates of $A$, $B$ and $C$, we can't give the numerical coordinates of the final - reflected triangle, but the general process is as described above.