Points A’, B', and ' are the images of 180-degree rotations of A, B, and C, respectively, around point 0. MB
C'
А
A
799
35°
0
С
B
Answer each question and explain your reasoning without measuring segments or angles.
1.
Name a segment whose length is the same as segment AO.
2.
What is the measure of angle A'OB'?

otation of a point through 180°, about the origin 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). Find the co-ordinates of the points obtained on rotating the points given below through 180° about the origin.(i) A (3, 5)            

(ii) B (-2, 7)          

(iii) C (-5, -8)      

(iv) D (9, -4)

Solution:

When rotated through 180° anticlockwise or clockwise about the origin, the new position of the above points is.

(i) The new position of the point A (3, 5) will be A' (-3, -5) ii) The new position of the point B (-2, 7) will be B' (2, -7) (iii) The new position of the point C (-5, -8) will be C' (5, 8)

(iv) The new position of the point D (9, -4) will be D' (-9, 4)

2. Plot the point M (-1, 4) on the graph paper and rotate it through 180° in the anticlockwise direction about the origin O. Find the new position of M.

Solution:

180 Degree Rotation

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When rotated through 180° in the anticlockwise direction about the origin O, then M (-1, 4) → M'' (1, -4).

3. Draw a line segment joining the point P (-3, 1) and Q (2, 3) on the graph paper and rotate it through 180° about the origin in anticlockwise direction.

Solution:

180 Degree Rotation about the Origin

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On plotting the points P (-3, 1) and Q (2, 3) on the graph paper to get the line segment PQ.

Now rotate PQ through 180° about the origin O in anticlockwise direction, the new position of points P and Q is:

P (-3, 1) → P' (3, -1)

Q (2, 3) → Q' (-2, -3)

Thus, the new position of line segment PQ is P'Q'.

Step-by-step explanation: