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प्रश्न
Using a graph paper, plot the points A (6,4) and B (0,4).
(i) Reflect A and B in the origin to get the images A’ and B’.
(ii) Write the co-ordinates of A’ and B’.
(iii) State the geometrical name for. the figure ABA’B’.
(iv) Find its perimeter.
उत्तर
(i) 
(ii) A' (-6, -4) and B' (0, -4)
(iii) ABA'B' is a parallelogram.
(iv) From the figure AB = 6, BB' = 8, A'B' = 6
In ΔABB', (AB)2
= (AB)2 + (BB')2
= 62 + 82
= 100
∴ AB' = 10 = A'B' ...{ABA'B' is a parallelogram}
∴ Perimeter of ABA'B'
= AB + BA' + A'B' + B'A
= 6 + 10 + 6 + 10
= 32 units.
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संबंधित प्रश्न
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(a, b) is first reflected in the origin and then reflected in the y-axis to P’. If P’ has co-ordinates (4, 6); evaluate a and b.
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”.
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.
Point A ( 4,-1) is reflected as A' in the line x= 1. Point B on reflection in the line y=3 is mapped as B' (6,-1). Write the co-ordinates of A' and B. Write the co-ordinates of mid.-ooint of the line sgment A' B'.
The image of a point P under reflection on the X-axis is (5, – 2). Write down the co-ordinates of P.
Point A(4, – 1) is reflected as A’ on Y-axis. Point B on refletion on X-axis is mapped as B’ (- 2, 5).
(i) Write the co-ordinates of A’.
(ii) Write the co-ordinates of B.
(iii) Write the co-ordinates of the middle point
M of the segment A’B.
(iv) Write the co-ordinates of the point of reflection A” of A on X-axis.
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.
Using graph paper and taking 1 cm = 1 unit along both x-axis and y-axis.
(i) Plot the points A (- 4, 4) and B (2, 2).
(ii) Reflect A and B in the origin to get the images A’ and B’ respectively.
(iii) Write down the co-ordinates of A’ and B’.
(iv) Give the geometrical name for the figure ABA’B’.
(v) Draw and name its lines of symmetry.
Use graph paper to answer this question:
(i) Plot the points A (4,6) and B (1, 2).
(ii) A’ is the image of A when reflected in X-axis,
(iii) B’ is the image of B when B is reflected in the line AA’.
(iv) Give the geometrical name for the figure ABA’B’.
