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प्रश्न
Point A (1 , -5) is mapped as A' on rflection in the line y = 1. The point B (-5 , 1) is mapped as B' on reflection in the line y = 4. Write the co-ordinaes of A' and B' . Calculate AB'.
उत्तर
A (1 , -5) , he co-ordinate of A' = (1 , 2 × 1 - (- 5)) = (1 , 7)
B (-5 , 1) , the co-ordinate of B' = (-5 , 2 × 4 - (1)) = (-5 , 7)
The distance AB' = `sqrt ((-5-1)^2 + (7 - (-5))^2)`
=`sqrt ((-6)^2 + 12^2)`
= `sqrt (36 + 144)`
= `sqrt 180`
= 13.41 units
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संबंधित प्रश्न
The point A(–3, 2) is reflected in the x-axis to the point A’. Point A’ is then reflected in the origin to point A”.
- Write down the co-ordinates of A”.
- Write down a single transformation that maps A onto A”.
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.
The image of a point P under reflection on the X-axis is (5, – 2). Write down the co-ordinates of P.
Using a graph paper, plot the points A (6,4) and B (0,4).
(i) Reflect A and B in the origin to get the images A’ and B’.
(ii) Write the co-ordinates of A’ and B’.
(iii) State the geometrical name for. the figure ABA’B’.
(iv) Find its perimeter.
(i) Find the reflection of the point (3, 5) on X-axis.
(ii) Find the reflection of the point (- 3, 5) on X-axis.
(iii) Find the reflection of the point (- 3, – 5) on X-axis.
(iv) Find the reflection of the point (3, – 5) on X-axis.
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”.
A point P(a, b) is reflected in the X-axis to P'(2, – 3). Write down the value of a & b. P” is the image of P, when reflected on the Y-axis. Write down the co-ordinates of P” when P is reflected in the line parallel to the Y-axis, such that x = 4.
Use a graph paper for this question. (Take 10 small divisions = 1 unit on both axis). P and Q have co-ordinates (0, 5) (- 2, 4).
(i) P is invariant when reflected in an axis. Name the axis.
(ii) Find the image of Q on reflection in the axis found in (i).
(iii) (0, k) on reflection in the origin is invariant. Write the value of k.
(iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin following by reflection in x-axis.
Use graph paper for this question.
The point P (5, 3) was reflected in the origin to get the image P’.
(i) Write down the co-ordinates of P’.
(ii) If M is the foot of the perpendicular from of P to the X-axis, find the co-ordinates of M.
(iii) If N is the foot of the perpendicular from of P’ to the X-axis, find the co-ordinates of N.
(iv) Name the figure PMP’N.
(v) Find the area of die figure PMP’N.
