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प्रश्न
Use a graph paper for this question (take 10 small divisions = 1 unit on both axis).
Plot the points P (3, 2) and Q (-3, -2), from P and Q draw perpendicular PM and QN on the X- axis.
(i) Name the image of P on reflection at the origin.
(ii) Assign, the. special name to the geometrical figure. PMQN and find its area.
(iii) Write the co-ordinates of the point to which M is mapped on reflection in (i) X- axis,
(ii) Y-axis, (iii) origin.
उत्तर
In the graph paper
(i) Q (-3, -2)
(ii) Parallelgoram;
Area of ΔPMN
= `(1)/(2) "PM" xx "MN"`
= `(1)/(2) xx 2 xx 63`
∴ Area of PMQN
= 2 x ΔPMN
= 2 x 6
= 12 square unit
(iii) Co-ordinates of M(3, 0)
(i) (3, 0), (ii) (-3, 0), (iii) (-3, 0).
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संबंधित प्रश्न
State the co-ordinates of the following point under reflection in the line y = 0:
(–3, 0)
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”.
P and Q have co-ordinates (–2, 3) and (5, 4) respectively. Reflect P in the x-axis to P’ and Q in the y-axis to Q’. State the co-ordinates of P’ and Q’.
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
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:
(2, 7)
State the co-ordinates of the images of the following point under reflection in the origin:
(9,-9)
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.
