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. click to select polygon abc

Explanation:

Step1: Recall x - axis reflection rule

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

Since no specific coordinates are given, the general steps for the double - reflection are as above. If we assume the coordinates of $A=(x_A,y_A)$, $B=(x_B,y_B)$ and $C=(x_C,y_C)$:

1. After reflection over the x - axis: $A'=(x_A,-y_A)$, $B'=(x_B,-y_B)$, $C'=(x_C,-y_C)$
2. After reflection of $\triangle A'B'C'$ over the y - axis: $A''=(-x_A,-y_A)$, $B''=(-x_B,-y_B)$, $C''=(-x_C,-y_C)$

Answer:

The vertices of the final reflected triangle are obtained by first changing the sign of the y - coordinates of the original triangle's vertices and then changing the sign of the x - coordinates of the resulting triangle's vertices.