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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.
APPEARS IN
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) |
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.
State the co-ordinates of the following point under reflection in y-axis:
(6, –3)
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”.
A point P is reflected in the x-axis. Co-ordinates of its image are (8, −6). Find the co-ordinates of P. Find the co-ordinates of the image of P under reflection in the y-axis.
Find the co-ordinates of the image of S(4,-1) after reflection in the line
x = 0
(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.
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 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.
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’.
