Practice the questions given in the worksheet on 180 degree rotation in anticlockwise direction or clockwise direction about the origin. The questions are based on how to rotate a shape about the origin 180° counter-clockwise direction or clockwise direction and find its new co-ordinates.

**1.** Plot the following points on the graph paper. Find the new position of each of these points when rotate through 180° about the origin.

(i) P (0, 9)

(ii) Q (-7, 5)

(iii) R (-6, -4)

(iv) S (2, 0)

**2.** Draw a square PQRS with its vertices (-2, 3); (2, 3); (2, -1) and (-2, -1) respectively. Rotate it through 180° anticlockwise about the origin O and find the co-ordinates to construct a new square P'Q'R'S'.

**3.** Find the new position of the following points when
rotated through 180° about the origin.

(i) A (-5, 4)

(ii) B (-2, -1)

(iii) C (3, -4)

(iv) D (5, 9)

**4.** Plot the point
A (-4, 2), B (2, 3), C (-2, -4) on the graph paper. Rotate the triangle ABC
through 180° about origin to the position A'B'C'. Find the co-ordinates of
points A'B'C'.

**5.** Plot the
points X (-5, -2) and Y (-1, 7) on the graph paper. Join XY. Rotate the line
segment XY about the origin through 180° and write the co-ordinates of X' and Y'.

Answers for the worksheet on 180 degree rotation are given below to check the exact answers of the above questions for finding the new position when the point is rotated through 180° about the origin.

**Answers:**

**1.** (i) P' (0, -9)

(ii) Q' (7, -5)

(iii) R' (6, 4)

(iv) S' (-2, 0)

**2.** P' (2, -3); Q'
(-2, -3); R' (-2, 1) and S' (2, 1)

**3.** (i) A' (5, -4)

(ii) B' (2, 1)

(iii) C' (-3, 4)

(iv) D' (-5, -9)

**4.** A' (4, -2), B'
(-2, -3) and C' (2, 4)

**5.** X' (5, 2) and
Y' (1, -7)

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