Question

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

Answer 1

Answer:

C) Reflection across the x-axis.

Step-by-step explanation:

From Linear Algebra we define the reflection across the x-axis is for $P(x,y) =(x,y)$:

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

If we know that $A(x,y) = (-1, 2)$, $B(x,y) =(-1,5)$, $C(x,y) = (-3, 5)$ and $D(x,y) =(-3, 2)$, then the reflected points are, respectively:

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

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

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

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

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