How do I find the center and angle of rotation

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Step-by-step explanation:

In general, if PQ is rotated to P'Q', the center of rotation (O) will be the point of intersection of the perpendicular bisectors of PP' and QQ'. The angle of rotation will be the angle POP', or QOQ'.

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The correspondence between preimage vertices ABCD and image vertices can be found by naming the vertices in the same order (clockwise) from one whose correspondence you know.

Here, the correspondence between A and W is given. Vertices clockwise from W are WXYZ, so those are the image points corresponding to ABCD.

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We note that the midpoints of AW and BX are coincident at the origin. That is, the perpendicular bisectors of these segments are coincident at the origin, so the origin (point O) is the center of rotation. The rotation angle is AOW, an angle that measures 180°.

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The image point coordinates are the opposites of the preimage point coordinates.

  A(2, 2) ⇒ W(-2, -2)

  B(2, 5) ⇒ X(-2, -5)

  C(5, 5) ⇒ Y(-5, -5)

  D(5, 2) ⇒ Z(-5, -2)

This is another indication that the rotation is 180° about the origin, since that rotation results in the mapping ...

  (x, y) ⇒ (-x, -y) . . . . . rotation 180° about the origin

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Step-by-step explanation:

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