Question

which reflection will produce an image of △rst with a vertex at (2, -3)? a reflection of △rst across the x - axis a reflection of △rst across the y - axis a reflection of △rst across the line y = x a reflection of △rst across the line y = -x

Explanation:

Step1: Recall reflection rules

Reflection across $x - axis$: $(x,y)\to(x, - y)$. Reflection across $y - axis$: $(x,y)\to(-x,y)$. Reflection across $y = x$: $(x,y)\to(y,x)$. Reflection across $y=-x$: $(x,y)\to(-y,-x)$.

Step2: Check each option for vertex transformation

For reflection across $x - axis$:

• For $R(-1,3)\to(-1, - 3)$, $S(3,-2)\to(3,2)$, $T(1,-4)\to(1,4)$.

For reflection across $y - axis$:

• For $R(-1,3)\to(1,3)$, $S(3,-2)\to(-3,-2)$, $T(1,-4)\to(-1,-4)$.

For reflection across $y = x$:

• For $R(-1,3)\to(3,-1)$, $S(3,-2)\to(-2,3)$, $T(1,-4)\to(-4,1)$.

For reflection across $y=-x$:

• For $R(-1,3)\to(-3,1)$, $S(3,-2)\to(2,-3)$, $T(1,-4)\to(4,-1)$.

Answer:

a reflection of $\triangle RST$ across the line $y = -x$