determining an image
which reflection will produce an image of $ \triangle r s t $ with a
vertex at $ (2,-3) $ ?
$ \bigcirc $ a reflection of $ \triangle r s t $ across the $ x $-axis
$ \bigcirc $ a reflection of $ \triangle r s t $ across the $ y $-axis
$ \bigcirc $ a reflection of $ \triangle r s t $ across the line $ y=x $
$ \bigcirc $ a reflection of $ \triangle r s t $ across the line $ y=-x $

Question

Accepted Answer

# Answer:
D. a reflection of $\triangle RST$ across the line $y = -x$

# Explanation:
## Step1: Recall the reflection formula
The formula for reflecting a point $(x,y)$ across the line $y=-x$ is $(x,y)\to(-y, -x)$

## Step2: Apply the formula to each vertex
- For $R(-1,3)$: $(-1,3)\to(-3,1)$
- For $S(3,-2)$: $(3,-2)\to(2,-3)$
- For $T(1,-4)$: $(1,-4)\to(4,-1)$

Since reflecting $S(3, - 2)$ across the line $y=-x$ gives the point $(2,-3)$, a reflection of $\triangle RST$ across the line $y = -x$ will produce an image of $\triangle RST$ with a vertex at $(2,-3)$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the reflection formula

Step2: Apply the formula to each vertex

Answer: