Advertisements
Advertisements
प्रश्न
The triangle ABC, where A is (2, 6), B is (–3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A"B"C".
- Write down the co-ordinates of A", B" and C".
- Write down a single transformation that maps triangle ABC onto triangle A"B"C".
उत्तर
i. Reflection in y-axis is given by My (x, y) = (–x, y)
∴ A’ = Reflection of A(2, 6) in y-axis = (–2, 6)
Similarly, B’ = (3, 5) and C’ = (–4, 7)
Reflection in origin is given by MO (x, y) = (–x, –y)
∴ A” = Reflection of A’(–2, 6) in origin = (2, –6)
Similarly, B” = (–3, –5) and C” = (4, –7)
ii. A single transformation which maps triangle ABC to triangle A”B”C” is reflection in x-axis.
APPEARS IN
संबंधित प्रश्न
Points (3, 0) and (–1, 0) are invariant points under reflection in the line L1; points (0, –3) and (0, 1) are invariant points on reflection in line L2.
- Name or write equations for the lines L1 and L2.
- Write down the images of the points P (3, 4) and Q (–5, –2) on reflection in line L1. Name the images as P’ and Q’ respectively.
- Write down the images of P and Q on reflection in L2. Name the images as P” and Q” respectively.
- State or describe a single transformation that maps P’ onto P''.
- Point P (a, b) is reflected in the x-axis to P’ (5, –2). Write down the values of a and b.
- P” is the image of P when reflected in the y-axis. Write down the co-ordinates of P”.
- Name a single transformation that maps P’ to P”.
The points P (4, 1) and Q (–2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.
A point P (–2, 3) is reflected in line x = 2 to point P’. Find the co-ordinates of P’.
- Plot the points A (3, 5) and B (–2, –4). Use 1 cm = 1 unit on both the axes.
- A’ is the image of A when reflected in the x-axis. Write down the co-ordinates of A’ and plot it on the graph paper.
- B’ is the image of B when reflected in the y-axis, followed by reflection in the origin. Write down the co-ordinates of B’ and plot it on the graph paper.
- Write down the geometrical name of the figure AA’BB’.
- Name the invariant points under reflection in the x-axis.
The point P (3, 4) is reflected to P’ in the x-axis; and O’ is the image of O (the origin) when reflected in the line PP’. Write:
- the co-ordinates of P’ and O’.
- the length of the segments PP’ and OO’.
- the perimeter of the quadrilateral POP’O’.
- the geometrical name of the figure POP’O’.
A (1, 1), B (5, 1), C (4, 2) and D (2, 2) are vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A’, B’, C’ and D’ respectively. Locate A’, B’, C’ and D’ on the graph sheet and write their co-ordinates. Are D, A, A’ and D’ collinear?
A’ and B’ are images of A (-3, 5) and B (-5, 3) respectively on reflection in y-axis. Find: (
a) the co-ordinates of A’ and B’.
(b) Assign special name of quadrilateral AA’B’B.
(c) Are AB’ and BA’ equal in length?
Use graph paper for this question.
(Take 2 cm = 1 unit along both x-axis and y-axis.)
Plot the points O(0, 0), A(–4, 4), B(–3, 0) and C(0, –3).
- Reflect points A and B on the y-axis and name them A' and B' respectively. Write down their co-ordinates.
- Name the figure OABCB'A'.
- State the line of symmetry of this figure.
Points (3, 0) and (-1, 0) are invarient points under reflection in the line L1; point (0, -3) and (0, 1) are invarient points on reflection in line L2.
(i) Write the equation of the line L1 and L2.
(ii) Write down the images of points P(3, 4) and Q(-5, -2) on reflection in L1. Name the images as P' and Q' respectively.
(iii) Write down the images of P and Q on reflection in L2. Name the image as P'' and Q'' respectively.
