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प्रश्न
The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A’B’C’. Triangle A’B’C’ is then reflected in the origin to triangle A”B”C”.
(i) Write down the co-ordinates of A”, B” and C”.
(ii) Write down a single transformation that maps triangle ABC onto triangle A”B”C”.
उत्तर
(i) Reflection in y-axis is given by My (x, y) = (-x, y)
∴ A’ = Reflection of A (2, 6) in y-axis = (-2, 6)
Similarly, B’ = (3, 5) and C’ = (-4, 7)
Reflection in origin is given by MO (x, y) = (-x, -y)
∴ A” = Reflection of A’ (-2, 6) in origin = (2, -6)
Similarly, B” = (-3, -5) and C” = (4, -7)
(ii) A single transformation which maps triangle ABC to triangle A”B”C” is reflection in x-axis.
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संबंधित प्रश्न
State the co-ordinates of the following point under reflection in the line y = 0:
(–3, 0)
Find the image of point (4, -6) under the following operations:
(i) Mx . My (ii) My . Mx
(iii) MO . Mx (iv) Mx . MO
(v) MO . My (vi) My . MO
Write down a single transformation equivalent to each operation given above. State whether:
(a) MO . Mx = Mx . MO
(b) My . MO = MO . My
Point A (4, –1) is reflected as A’ in the y-axis. Point B on reflection in the x-axis is mapped as B’ (–2, 5). Write down the co-ordinates of A’ and B.
State the co-ordinates of the images of the following point under reflection in the origin:
(-1,-4)
State the co-ordinates of the images of the following point under reflection in the origin:
(0, 2)
Find the co-ordinates of the images of the following under reflection in the origin:
(3, -7)
Find the co-ordinates of the images of the following under reflection in the origin:
`((-5)/(2),(-1)/(2))`
Point A (2, -4) is reflected in origin as A’. Point B (- 3, 2) is reflected on X-axis as B’.
(i) Write the co-ordinates of A’.
(ii) Write the co-ordinates of B’.
(iii) Calculate the distance A’B’.
Give your answer correct to 1 decimal place, (do not consult tables).
The image of triangle OXY under reflection in the origin, O is the triangle OX1Y1, where X1(-3, -4) is the image of X and Y1, (0, -5) is the image of Y.
(i) Draw a diagram to represent this information and write down the co-ordinates of X and Y.
(ii) What kind of figure is the quadrilateral XYX1Y1? Give reason for your answer. State, with a reason, whether the figure XYX1Y1 has any lines of symmetry.
(iii) Find the co-ordinates of X2, the image of X under reflection in the origin followed by reflection on the Y-axis.
(iv) Find the co-ordinates of Y2, the image of Y under reflection on the X-axis followed by reflection in the origin.
Use graph paper for this question.
The points A (2, 3), B (4, 5) and C (7, 2) are the vertices of A ABC.
- Write down the coordinates of A’, B’, C’ if Δ A’B’C’ is the image of Δ ABC, when reflected in the origin.
- Write down the co-ordinates of A”, B”, C” if A” B” C” is the image of Δ ABC, when reflected in the x-axis.
- Mention the special name of the quadrilateral BCC” B” and find its area.
