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प्रश्न
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.
उत्तर
(i) Reflection in origin
\[\ce{(x, y) ->[M0]=(-x, -y)}\]
∴ \[\ce{A(2, 3) ->[M0]= A'(-2, -3)}\]
\[\ce{B(4, 5) ->[M0]= B'(-4, -5)}\]
\[\ce{C(7, 2) ->[M0]= C'(-7, -2)}\]
(ii) Now A, B, C is reflected in X axis.
Reflection in X axis
\[\ce{(x, y)->[Mx]=(x, -y)}\]
∴ \[\ce{A(2, 3)->[Mx]=A^"(2, -3)}\]
\[\ce{B(4, 5)->[Mx]=B^"(4, -5)}\]
\[\ce{C(7, 2)->[Mx]=C^"(7, -2)}\]
(iii) BCC"B" is an isosceles trapezium.
CD = 7 - 4 = 3
CC" = 2 + 2 = 4 and
BB" = 5 + 5 = 10
Area of Trapexium = `(1)/(2)` (CC" + BB") x CD
= `(1)/(2)` (10 + 4) x 3
= `(1)/(2)` x 14 x 3
= 21 sq. unit
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संबंधित प्रश्न
State the co-ordinates of the following point under reflection in origin:
(–2, –4)
State the co-ordinates of the following point under reflection in the line y = 0:
(–3, 0)
A point P is reflected in the origin. Co-ordinates of its image are (–2, 7). Find the co-ordinates of P.
On a graph paper, plot the triangle ABC, whose vertices are at the points A (3, 1), B (5, 0) and C (7, 4).
On the same diagram, draw the image of the triangle ABC under reflection in the origin O (0, 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
The point (–5, 0) on reflection in a line is mapped as (5, 0) and the point (–2, –6) on reflection in the same line is mapped as (2, –6).
- Name the line of reflection.
- Write down the co-ordinates of the image of (5, –8) in the line obtained in (a).
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)
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 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.
