Question

1. reflection: across the line y = 2 x - axis

Explanation:

Step1: Recall reflection rule

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

Step2: Identify vertices of triangle

The vertices of the given triangle are $(1,1)$, $(1,4)$ and $(5,3)$.

Step3: Apply reflection rule to each vertex

For $(1,1)$: $(1,1)\to(1,-1)$; for $(1,4)$: $(1,4)\to(1, - 4)$; for $(5,3)$: $(5,3)\to(5,-3)$.

Answer:

The new vertices of the reflected triangle are $(1,-1)$, $(1,-4)$ and $(5,-3)$.