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प्रश्न
- 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.
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उत्तर
- The points A (3, 5) and B (–2, –4) can be plotted on a graph as shown.
- A’ = Image of A when reflected in the x-axis = (3, –5)
- C = Image of B when reflected in the y-axis = (2, –4) B’ = Image when C is reflected in the origin = (–2, 4)
- Isosceles trapezium
- Any point that remains unaltered under a given transformation is called an invariant. Thus, the required two points are (3, 0) and (–2, 0).
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संबंधित प्रश्न
The point (–2, 0) on reflection in a line is mapped to (2, 0) and the point (5, –6) on reflection in the same line is mapped to (–5, –6).
- State the name of the mirror line and write its equation.
- State the co-ordinates of the image of (–8, –5) in the mirror line.
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’.
A point P (a, b) is reflected in the x-axis to P’ (2, –3). Write down the values of a and b. P” is the image of P, reflected in the y-axis. Write down the co-ordinates of P”. Find the co-ordinates of P”’, when P is reflected in the line, parallel to y-axis, such that x = 4.
Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:
- A’ of A under reflection in the x-axis.
- B’ of B under reflection in the line AA’.
- A” of A under reflection in the y-axis.
- B” of B under reflection in the line AA”.
The point P (5, 3) was reflected in the origin to get the image P’.
- Write down the co-ordinates of P’.
- If M is the foot of the perpendicular from P to the x-axis, find the co-ordinates of M.
- If N is the foot of the perpendicular from P’ to the x-axis, find the co-ordinates of N.
- Name the figure PMP’N.
- Find the area of the figure PMP’N.
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?
P and Q have co-ordinates (0, 5) and (–2, 4).
- P is invariant when reflected in an axis. Name the axis.
- Find the image of Q on reflection in the axis found in (a).
- (0, k) on reflection in the origin is invariant. Write the value of k.
- Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x-axis.
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.
