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प्रश्न
The point A(–3, 2) is reflected in the x-axis to the point A’. Point A’ is then reflected in the origin to point A”.
- Write down the co-ordinates of A”.
- Write down a single transformation that maps A onto A”.
उत्तर
i. The reflection in x-axis is given by Mx (x, y) = (x, –y).
A’ = reflection of A(–3, 2) in the x-axis = (–3, –2).
The reflection in origin is given by MO (x, y) = (–x, –y).
A” = reflection of A’(–3, –2) in the origin = (3, 2)
ii. The reflection in y-axis is given by My (x, y) = (–x, y).
The reflection of A(–3, 2) in y-axis is (3, 2).
Thus, the required single transformation is the reflection of A in the y-axis to the point A”.
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संबंधित प्रश्न
State the co-ordinates of the following point under reflection in x-axis:
(3, 2)
A point P is reflected in the x-axis. Co-ordinates of its image are (–4, 5). Find the co-ordinates of the image of P under reflection in the y-axis.
The point P(x, y) is first reflected in the x-axis and reflected in the origin to P’. If P’ has co-ordinates (–8, 5); evaluate x and y.
P' is the image of P under reflection in the x-axis. If the co-ordinates of P' are (2, 10), write the co-ordinates of P.
S' is the image of S under reflection in the origin. If the co-ordinates of S are (2,-5), write the co-ordinates of S'.
A triangle ABC lies in the co-ordinate plane. The co-ordinates of its vertices are A (2, 3), B ( 4,-4) and C (6 ,-7). This triangle is reflected in the line y=O onto LA'B'C'. LA'B'C' is then reflected in the origin ontolA"B"C". Write down the co-ordinates of LA'B'C' and LA "B" C".
Find the co-ordinates of the image of A (-5, 4) after reflection in the line
y = 4
Find the co-ordinates of the image of S(4,-1) after reflection in the line
x = 0
Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axis). P and Q have co-ordinates (0, 5) (- 2, 4).
(i) P is invariant when reflected in an axis. Name the axis.
(ii) Find the image of Q on reflection in the axis found in (i).
(iii) (0, k) on reflection in the origin is invariant. Write the value of k.
(iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin following by reflection in x-axis.
