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2 October, 09:58

What set of transformations could be applied to rectangle ABCD to create A'B'C'D'?

Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle transformed formed by ordered pairs A prime at negative 4, negative 2, B prime at negative 4, negative 1, C prime at negative 1, negative 1, D prime at negative 1, negative 2. Reflected over the x-axis and rotated 180° Reflected over the y-axis and rotated 180° Reflected over the x-axis and rotated 90° counterclockwise Reflected over the y-axis and rotated 90° counterclockwise

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  1. 2 October, 12:48
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    Reflection over the y-axis and rotation of 180°

    Step-by-step explanation:

    We have,

    Rectangle ABCD with co-ordinates A (-4,2), B (-4,1), C (-1,1) and D (-1,2).

    It is transformed to a new rectangle A'B'C'D' with co-ordinates A' (-4,-2), B' (-4,-1), C' (-1,-1) and D' (-1,-2).

    The graph of both the triangles is shown below.

    We see that,

    The rectangle ABCD is reflected about y-axis and then rotated 180° to obtain A'B'C'D'.

    Reflected about y-axis Rotation of 180°

    A = (-4,2) (4,2) A' = (-4,-2)

    B = (-4,1) (4,1) B' = (-4,-1)

    C = (-1,1) (1,1) C' = (-1,-1)

    D = (-1,2) (1,2) D' = (-1,-2)

    Hence, the second rectangle is formed by: Reflection over the y-axis and rotation of 180°.
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