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प्रश्न
P, Q have co-ordinates (-1, 2) and (6, 3) respectively. Reflect P on the X-axis to P’. Find:
(i) The co-ordinate of P’
(ii) Length of P’Q.
(iii) Length of PQ.
(iv) Is P’Q = PQ?
उत्तर
(i) P' → (-1 -2).
(ii) P'Q = `sqrt((6 + 1)^2 + (3 + 2)^2)`
= `sqrt(49 + 25)`
= `sqrt(74)`.
(iii) PQ = `sqrt((6 + 1)^2 + (3 - 2)^2)`
= `sqrt(49 + 1)`
= `sqrt(50)`.
(iv) No. (P'Q ≠ PQ)
APPEARS IN
संबंधित प्रश्न
State the co-ordinates of the following point under reflection in the line x = 0:
(–6, 4)
A point P is reflected in the origin. Co-ordinates of its image are (–2, 7). Find the co-ordinates of the image of P under reflection in the x-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.
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.
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 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".
Find the co-ordinates of the image of S(4,-1) after reflection in the line
x = 0
Write down the co-ordinates of the image of (5, – 4).
Reflection in x = 0;
A point P(4, – 1) is reflected to P’ in the line y = 2 followed by the reflection to P” in the line x = -1. Find :
(i) The co-ordinates of P’.
(ii) The co-ordinates of P”.
(iii) The length of PP’.
(iv) The length of P’P”.
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.
