Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below: A(-1,2) B(-1,5) C(-3,5) D(-3,2) A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2) What transformation did Kim perform to create rectangle A'B'C'D? (5 points)
A)Reflection across the y-axis
B)Rotation of 270 degrees counterclockwise about the origin
C)Reflection across the x-axis
D)Rotation of 90 degrees counterclockwise about the origin

This question is based on the reflection of x- axis. Hence the correct answer is C, reflection across the x-axis.

Given:

Transform  rectangle ABCD to rectangle A'B'C'D',

The vertices of rectangle ABCD is A(-1,2) B(-1,5) C(-3,5) D(-3,2).

The vertices of rectangle A'B'C'D is A'(-1,-2) B'(-1,-5) C'(-3,-5) D'(-3,-2).

We need to determined the transformation that Kim perform to create rectangle A'B'C'D.

From Linear Algebra we define the reflection across the x-axis is for,

P(x,y) = (x,y)

P(x,y) = (x,-y)                                (1)

It is given that  A(-1,2), B(-1,5), C(-3,5) and D(-3,2).

Therefore from equation (1)  above point becomes,

A'(x,y) = (-1,-2)

B'(x,y) =(-1,-5)

C'(x,y) =(-3,-5)

D'(x,y) =(-3,-2)

Therefore, It is observe that Kim performed a reflection across the x-axis to create triangle A'B'C'D'. Hence the correct answer is C, reflection across the x-axis.

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C) Reflection across the x-axis.

Step-by-step explanation:

From Linear Algebra we define the reflection across the x-axis is for :

(1)

If we know that , , and , then the reflected points are, respectively:

In consequence, Kim performed a reflection across the x-axis to create triangle A'B'C'D'. The correct answer is C.

step-by-step explanation:

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