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प्रश्न
The point P(3, 4) is reflected to P’ in the x-axis and O’ is the image of O (the Origin) in the line PP’ Find :
(i) The coordinates of P’ and O’.
(ii) The length of segment PP’ and OO’.
(iii) The perimeter of the quadrilateral POP’O’
(iv) What is the special name of the quadrilateral POP’O’.
उत्तर
(i) P' (3, -4), O'(6, 0)
(ii) PP'
= `sqrt((3 - 3)^2 + (-4 - 4)^2)`
= `sqrt(64)`
= 8 units
OO'
= `sqrt((0 - 6)^2 + (0 - 0)^2)`
= `sqrt(36)`
= 6 units.
(iii) Perimeter
= 5 + 5 + 5 + 5
= 20 units.
(iv) Rhombus.
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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 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.
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.
Point A (1,-5) is mapped as A' on reflection in the line y= l . The point B (-5, 1) is mapped as B' on reflection in the line y=4. Write the co-ordinates of A' and B'. Calculate AB'.
The image of a point P under reflection on the X-axis is (5, – 2). Write down the co-ordinates of P.
Point A (5, 1) on reflection on X- axis is mapped as A’. Also A on reflection on Y- axis is mapped as A”.
(i) Write the co-ordinates of A’.
(ii) Write the co-ordinates of A”.
(iii) Calculate the distance A’ A”.
(iv) On which coordinate axis does the middle point M of A” A’ lie?
Using graph paper and taking 1 cm = 1 unit along both x-axis and y-axis.
(i) Plot the points A (- 4, 4) and B (2, 2).
(ii) Reflect A and B in the origin to get the images A’ and B’ respectively.
(iii) Write down the co-ordinates of A’ and B’.
(iv) Give the geometrical name for the figure ABA’B’.
(v) Draw and name its lines of symmetry.
