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Rectangle LMNO has vertices L(–4,6), M(–1,6), N(–1,2), and O(–4,2). Suppose you first reflect this rectangle across the y-axis. Then, translate it down four units and to the left one unit. Where are the corresponding vertices L′M′N′O′ located?L′(–5,–10), M′(0,–10), N′(–2,–2), O′(–5,–6)L′(3,2), M′(0,2), N′(0,–2), O′(3,–2)L′(–5,–10), M′(–2,–10), N′(–2,–6), O′(–5,–2)L′(3,2), M′(0,–2), N′(0,2), O′(3,–2)

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L′(3,2), M′(0,2), N′(0,–2), O′(3,–2)

Step-by-step explanation

Step 1

plot the rectangle

Step 2

make the indicated transformations

a)

first reflect this rectangle across the y-axis:

The rule for the reflection around the Y axis is you basically just put a "negative" in front of the X coordinates of each point

so

Let


\begin{gathered} L(-4,6) \\ M(-1,6) \\ N(-1,2) \\ O(-4,2) \end{gathered}

then


\begin{gathered} L(-4,6)\Rightarrow L(-(-4),6)\Rightarrow L1=(4,6) \\ M(-1,6)\Rightarrow M(-(-1),6)\Rightarrow M1=(1,6) \\ N(-1,2)\Rightarrow N(-(-1),2)\Rightarrow N1=(1,2) \\ O(-4,2)\Rightarrow O(-(-4),2)\Rightarrow O1=(4,2) \end{gathered}

b) Then, translate it down four units and to the left one unit

To translate the point P(x,y) , a units right and b units up, use P'(x+a,y+b)

, if the traslation is down a is negative, if the translation is to the left, b is negative

hence

i) subtract 4 to the y-coordinate

ii)subtract 1 unit from x -axis ,so


(x,y)\Rightarrow(x-1,y-4)

therefore,


\begin{gathered} L1(4,6)\Rightarrow L^(\prime)=(4-1,6-4))=L^(\prime)(3,2) \\ M1(1,6)\Rightarrow M^{^(\prime)}=(1-1,6-4))=L^(\prime)(0,2) \\ N1(1,2)\Rightarrow N^(\prime)=(1-1,2-4))=N^(\prime)(0,-2) \\ O1(4,2)\Rightarrow O(4-1,2-4)\Rightarrow O1=O^(\prime)(3,-2) \end{gathered}

so,

the answer is

L′(3,2), M′(0,2), N′(0,–2), O′(3,–2)

I hope this helps you

Rectangle LMNO has vertices L(–4,6), M(–1,6), N(–1,2), and O(–4,2). Suppose you first-example-1
Rectangle LMNO has vertices L(–4,6), M(–1,6), N(–1,2), and O(–4,2). Suppose you first-example-2
Rectangle LMNO has vertices L(–4,6), M(–1,6), N(–1,2), and O(–4,2). Suppose you first-example-3
User Larry Silverman
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