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प्रश्न
Use a graph paper for this question.
(i) The point P (2, – 4) is reflected about the line x = 0 to get the image Q. Find the coordinates of Q.
(ii) Point Q is reflected about the line y = 0 to get the image R. Find the co-ordinates of R.
(iii) Name the figure PQR.
(iv) Find the area of figure PQR.
उत्तर
(i) P (2, – 4) is reflected in (x = 0) y-axis and Q-image.
\[\ce{P(2, -4) ->[My][]Q(-2, -4)}\]
(ii) Q (-2, -4) is reflected in (y = 0) x-axis to get R.
\[\ce{Q(2, -4) ->[Mx][]R (-2, -4)}\]
(iii) The figure PQR is right triangle as shown ahead:
(iv) Area of ΔPQR = `(1)/(2) xx "PQ" xx "QR"`
= `(1)/(2) xx 4 xx 8`
= 16 sq. unit.
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संबंधित प्रश्न
A point P is its own image under the reflection in a line l. Describe the position of point the P with respect to the line l.
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.
A point P is mapped onto P' under the reflection in the x-axis. P' is mapped onto P" under the reflection in the origin. If the co-ordinates of
P" are (5,-2), write down the co-ordinates of P. State the single transformation that takes place.
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".
A point P (-8, 1) is reflected in the x-axis to the point P'. The point P' is then reflected in the origin to point P". Write down the co-ordinates of P". State the single transformation that maps P into 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'.
Use a graph paper to answer the following questions. (Take 1 cm = 1 unit on both axis):
(i) Plot A (4, 4), B (4, – 6) and C (8, 0), the vertices of a triangle ABC.
(ii) Reflect ABC on the y-axis and name it as A’B’C’.
(iii) Write the coordinates of the images A’, B’ and C’.
(iv) Give a geometrical name for the figure AA’ C’B’ BC.
(v) Identify the line of symmetry of AA’ C’ B’ BC.
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’.
