Question

1 . Draw Δ1 at (4,7) , (8,5) . (8,7)
a . Rotate Δ1 90° clockwise , center (4,3) onto Δ2
b . Rotate Δ2 180° , center (5,-1) onto Δ3
c . Rotate Δ3 90° anticlockwise , center (0.-8) onto Δ4
d . Describe fully the following rotations
1 : Δ4 onto Δ1
2 : Δ4 onto Δ2

Answer 1

Answer:

Find the new position of the following points when rotated through 90° anticlockwise about the origin.

(i) A (2, 3)

(ii) B (-5, -7)

(iii) C (-6, 9)

(iv) D (4, -8)

Solution:

When rotated through 90° about the origin in anticlockwise direction. The new positions of the above points are:

(i) The new position of point A (2, 3) will become A' (-3, 2)

(ii) The new position of point B (-5, -7) will become B' (7, -5)

(iii) The new position of point C (-6, 9) will become C' (-9, -6)

(iv) The new position of point D (4, -8) will become D' (8, 4)

2. Draw a triangle ABC on the graph paper. The co-ordinate of A, B and C being A (1, 2), B (3, 1) and C (2, -2), find the new position when the triangle is rotated through 90° anticlockwise about the origin.

Solution:

90 Degree Anticlockwise Rotation

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Plot the points A (1, 2), B (3, 1) and C (2, -2) on the graph paper. Join AB, BC and Cato get a triangle. On rotating it through 90° about the origin in anticlockwise direction, the new position of the points are:

A (1, 2) will become A' (-2, 1)

B (3, 1) will become B' (-1, 3)

C (2, -2) will become C' (2, 2)

Thus, the new position of ∆ ABC is ∆ A'B'C'.