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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
Complete the following table:
| Point | Transformation | Image | |
| (a) | (5, –7) | -------------------- | (–5, 7) |
| (b) | (4, 2) | Reflection in x-axis | ------- |
| (c) | ------- | Reflection in y-axis | (0, 6) |
| (d) | (6, –6) | -------------------- | (–6, 6) |
| (e) | (4, –8) | -------------------- | (–4, –8) |
State the co-ordinates of the following point under reflection in y-axis:
(6, –3)
A point P is reflected in the x-axis. Co-ordinates of its image are (–4, 5). Find the co-ordinates of P.
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.
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 A (-5, 4) after reflection in the line
y = 4
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.
(i) Point P(a, b) reflected on the X-axis to P'(5, 2). Write down the value of a and b.
(ii) P” is the image of P when reflected on the Y-axis. Write down the co-ordinates of P”.
(iii) Name a single transformation that maps P’ to P”.
