On a coordinate plane, a trapezoid has points H prime (negative 3, negative 2), J prime (negative 2, negative 3), K prime (negative

On a coordinate plane, a trapezoid has points H prime (negative 3, negative 2), J prime (negative 2, negative 3), K prime (negative 3, negative 4), G prime (negative 5, negative 2). Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H? (2, 3) (–2, 3) (3, 2) (3, –2)

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  1. when a point M (h, k) is rotated about the origin O through 180° in anticlockwise or clockwise direction, it takes the new position M' (-h, -k). The signs of the coordinates change .

    In the given graph point H' is (-3,-2) .The pre image of this point will be point H .Point H will have coordinates which will have signs of both coordinates opposite to that  of point H'.

    Coordinates of point H will be (3,2)

    Step-by-step explanation:

  2. H(3,2)

    Step-by-step explanation:

    The missing diagram is shown in the attachment.

    The trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph.

    We want to determine the coordinates of the pre-image point H.

    From the diagram H' is located at (-3,-2).

    We know the rule for 180° rotation about the origin is :

    [tex](x,y)\to (-x,-y)[/tex]

    This means that:

    [tex]( - 3, - 2) = (-x,-y)[/tex]

    Equating corresponding components, we have -x=-3.

    This means that:

    x=3.

    Also, -y=-2, implies that y=2.

    Therefore the coordinates of the pre-image point H is (3,2)

    [tex]Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on[/tex]

  3. when a point M (h, k) is rotated about the origin O through 180° in anticlockwise or clockwise direction, it takes the new position M' (-h, -k). The signs of the coordinates change .

    In the given graph point H' is (-3,-2) .The pre image of this point will be point H .Point H will have coordinates which will have signs of both coordinates opposite to that  of point H'.

    Coordinates of point H will be (3,2)

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