Question

1 reflect across the x - axis. translate 5 units left.

Explanation:

Step1: Recall reflection rule

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

Step2: Recall translation rule

The rule for translating a point $(x,y)$ 5 units to the left is $(x - 5,y)$. After translating the reflected points $A'$, $B'$ and $C'$ 5 units to the left, the final vertices are $A''(x_1 - 5,-y_1)$, $B''(x_2 - 5,-y_2)$ and $C''(x_3 - 5,-y_3)$. For example, if $A=(3,6)$, $B=(5,1)$ and $C=(1,1)$:

• After reflection across the $x -$axis: $A'=(3,-6)$, $B'=(5,-1)$, $C'=(1,-1)$.
• After translation 5 units left: $A''=(3 - 5,-6)=(-2,-6)$, $B''=(5 - 5,-1)=(0,-1)$, $C''=(1 - 5,-1)=(-4,-1)$.

We would need to apply these rules to all the vertices of the given triangle to get the new - positioned triangle. But the general transformation steps are as above.

Answer:

Vertices of the new triangle are obtained by first reflecting the original vertices across the $x -$axis and then translating the reflected vertices 5 units to the left using the rules $(x,y)\to(x,-y)$ (reflection) and $(x,y)\to(x - 5,y)$ (translation).