Question

which reflection will produce an image of δrst with a vertex at (2, -3)? a reflection of δrst across the x - axis a reflection of δrst across the y - axis a reflection of δrst across the line y = x a reflection of δrst across the line y = -x r(-1, 3) s(3, -2) t(1, -4)

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

• Across $x - axis$: $(-1,3)\to(-1,-3)$
• Across $y - axis$: $(-1,3)\to(1,3)$
• Across $y = x$: $(-1,3)\to(3,-1)$
• Across $y=-x$: $(-1,3)\to(-3,1)$

Step3: Test point $S(3,-2)$

• Across $x - axis$: $(3,-2)\to(3,2)$
• Across $y - axis$: $(3,-2)\to(-3,-2)$
• Across $y = x$: $(3,-2)\to(-2,3)$
• Across $y=-x$: $(3,-2)\to(2,-3)$

Step4: Test point $T(1,-4)$

• Across $x - axis$: $(1,-4)\to(1,4)$
• Across $y - axis$: $(1,-4)\to(-1,-4)$
• Across $y = x$: $(1,-4)\to(-4,1)$
• Across $y=-x$: $(1,-4)\to(4,-1)$

Answer:

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