Question

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

Explanation:

Step1: Recall reflection rules

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

Step2: Analyze each option

For point $R(-1,3)$:

• Reflection across $y = x$ gives $(3,-1)$.
• Reflection across $y -$axis gives $(1,3)$.
• Reflection across $x -$axis gives $(-1,-3)$.
• Reflection across $y=-x$ gives $(-3,1)$.

For point $S(3,-2)$:

• Reflection across $y = x$ gives $(-2,3)$.
• Reflection across $y -$axis gives $(-3,-2)$.
• Reflection across $x -$axis gives $(3,2)$.
• Reflection across $y=-x$ gives $(2,-3)$.

Answer:

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